Jorge Pullin: Our speaker today is constantly in Ada who speak about super gravity and how to G.
Konstantin Eder: Yes, thank you for the introduction and thank you to the organizers for the invitation and the opportunity to present my right, which I did, in cooperation with Simon and which is about various aspects of super gravity gravity and what results you can find these papers.
Konstantin Eder: Okay, now, before I start with mean part of the talk, or like to give a brief introduction about what super gravity and actually is.
Konstantin Eder: is an interesting and interesting and context and context of gravity.
Konstantin Eder: And the core of super gravity is, of course, of a cemetery so let me just briefly say something about supersymmetry.
Konstantin Eder: Now, and the standard model It follows that the Channel channel either the algebra symmetries for the metrics when interacting quantum field theory is gigantic of his form, so you have the edge of space time symmetries.
Konstantin Eder: Space it's actually I draw from clusters based time and you have the symmetry which could be, for instance cage cemeteries.
Konstantin Eder: And, in particular, is the dark some of you have received drivel commentator between both generators.
Konstantin Eder: And this is a theorem of work, the Channel theorem and not common among law, which states that generically symmetries have this form.
Konstantin Eder: So the only way around seems to be one allows what not you kind of symmetry and this was the.
Konstantin Eder: observational Parker was transcribed so on ios there's this term does not apply it allows for new kind of find your boss or quarter created entrepreneurs so.
Konstantin Eder: We just said to grade algebra je je with some breakage which splits into two parts G not, which is the easy part of corporate sonic.
Konstantin Eder: Somewhat party, one which is called family Ionic and you have your commentator, which is the standard commentator on G, not in samantha commentator on G one, and you have some credit translation of the jacoby identity.
Konstantin Eder: This context and and also follows that the smallest possible algebra.
Konstantin Eder: which contains to space them symmetries super concrete algebra case of vanishing cosmological constant or the supervisor sit entrepreneurs P, one for in case of a.
Konstantin Eder: Non managed cosmological constant in both cases this is your spirits in this form, with gina blahnik part which is the dashboard space time symmetries and some odd part which is a Marianna presentation.
Konstantin Eder: And the eating part is generated grants space time translations and by Lawrence transmission to my day.
Konstantin Eder: And the odd part is generated by somebody on us.
Konstantin Eder: And he said his find his vision of creative connotation relations where the middle of this tells you that.
Konstantin Eder: This Marianna generator to other religions folks in terms of speed in terms of a spinner.
Konstantin Eder: And the second one relates them to space them that, for instance, missions and.
Abhay Vasant Ashtekar: Why the sitter is not allowed.
Konstantin Eder: yeah, this is a generic property a problem in the theory, so if you do not consider broken supersymmetry is then generically the only possibility to scribe supersymmetric theories.
Konstantin Eder: And you need a negative customer to customer.
Abhay Vasant Ashtekar: So, but one blazer on here if I just put out to myself or something I mean I don't know what the conventions that I.
Konstantin Eder: attended to me.
Abhay Vasant Ashtekar: So.
Konstantin Eder: Yes.
Abhay Vasant Ashtekar: Okay, thank you.
Carlo Rovelli: Is understanding is that the artist is of the of the column and Mandela theorem rule out the seat of essentially to start with.
Konstantin Eder: For.
Carlo Rovelli: Its among the importance of economy can you say there is an audience of algebra so it wants punk or a sister.
Abhay Vasant Ashtekar: No, no, but that I do disagree with allowed until it's if it also doesn't have translations right, so I was really trying to draw the visitor Center.
Carlo Rovelli: that's what.
Abhay Vasant Ashtekar: Okay yeah between discipline and discipline in this in this generalization of targets on yes.
Abhay Vasant Ashtekar: Thank you very much.
Konstantin Eder: As long as you're setting it's hard to.
Konstantin Eder: restrict theories for positive positive crossing the constant, but then, if you have more general theories.
Abhay Vasant Ashtekar: Thank.
Konstantin Eder: In case of a nomination a nomination, because we call Center get these additional contributions which are proportional so to some things K l which is.
Konstantin Eder: That since now we have these additional generators, they are particular and the commutative and they transform as being us, and so it follows that they interrelate particles of integer and half into to spin.
Konstantin Eder: And so they were a political says both hands and formulas so it's a symmetry among different particle different particular species.
Konstantin Eder: And also, we can include further from Munich generators new theory and this case you call this an extended.
Konstantin Eder: supersymmetry present the present talk about on many talk about and then one case because this the simplest one, and you can already thought of conclusions of the theory, the structure is, which is a test.
Konstantin Eder: Now, in case to applications to gravity, you can ask the question, if you have a locus of symmetry so if you're super serious automation space time dependent and that cuz This leads to super gravity.
Konstantin Eder: In the vehicle for in one case, it follows that this theory or contains a quotation field gravitational field, presented by gravity time and now has been a free half partner, which is the gravity.
Konstantin Eder: Now is the theory interesting.
Konstantin Eder: Oh, various various things to name here now one possibility because.
Konstantin Eder: This is a unified description between both sons and fireman's it is to identify description between my first metal particles, so this may provide a way to formulate potential for theories.
Konstantin Eder: And also, they appear in terms of low energy and energy demands of certain string theories.
Konstantin Eder: And they are proposals that the sticker for enclave maximum super gravity theory, maybe photography finite, which is due to the fact that.
Konstantin Eder: In the Center great case, this is the gravity theory, with a maximum possible amount of cemeteries so as the team is such a violent behavior, and this is why I suggest to this hospitality final criminal criminal very calculation so to justice.
Konstantin Eder: Pacific, if we look on gravity.
Konstantin Eder: France, because now, I have this tight connection between metal fire between force and metal particles.
Konstantin Eder: mentors not part of gravity and I can commit draw conclusions, how to quantify metal particles in front of quantum gravity.
Konstantin Eder: And also because there are some new developments which can be also used in gravity you see any theories, to make contact to ponder descriptions thing theories and the safety conjecture i've explained this at the end of my time.
Konstantin Eder: And also make contact to the black and black hole entropy calculations string theory which is related to proper definition of ups dates which are the central quantum states and in description of Superman supersymmetric black holes.
Konstantin Eder: Now they exist already various interesting resides in the literature preaching loop on gravity.
Konstantin Eder: Has treating super gravity in front of a frequent gravity.
Konstantin Eder: And, for instance jacobson extended this formulation of gravity in terms of us to conserve two variables to super gravity and also sula extended this tool arbitrary recovering music parameters.
Konstantin Eder: and studying the self to theory.
Konstantin Eder: But and constantly enterprise, it was observed by Philip and further has been a mini Oregon pulling that.
Konstantin Eder: There is some new symmetry in the theory summit and symmetry in theory.
Konstantin Eder: And, which corresponds to a credits entrepreneurs so but also tactic article is people want to.
Konstantin Eder: And then, using this observation and also.
Konstantin Eder: considered a former quantization of the theory exploiting the symmetry was considered thousand by convenient applicant putting also thinking smolan.
Konstantin Eder: Introducing the notion of the House peace be network.
Konstantin Eder: And the and small and also considered in a boundaries in this framework to describing a boundaries and practical super gravity using to quantum gravity techniques.
Konstantin Eder: And then also this observation of this underlying wispy cage symmetry was used in context of spin for models and equal three other get order to get an idea how to quantify formulas in his mouth was considered by living attacker and also Ryan budget.
Konstantin Eder: And finally potent off tomorrow to.
Konstantin Eder: succeeded in extending the theory, the construction of the theory to arbitration and higher space time dimensions, introducing a new kind of variables.
Konstantin Eder: And also take succeeded in quantitative research ring I feared, and also hire people engaged fields which play a particular important role for higher dimensional sort of gravity.
Konstantin Eder: But there are still various open questions, one has to consider in the gravity.
Konstantin Eder: One part main part is of course the dynamics because super gravity, you have a new constraint, which governs the dynamics Actually, this is an interesting part because this also can make on contact to the standard colonization procedures hamiltonian constraint.
Konstantin Eder: of symmetry just models can be considered as possible because indications.
Konstantin Eder: Martin fundamental side.
Konstantin Eder: has to do with the question Where does this large symmetry which.
Konstantin Eder: One which one themselves in the algebra.
Konstantin Eder: actually come from and whether this is a generic feature that can be extended to.
Konstantin Eder: Two more general channel super gravity's theories now whether this is really just a property of the self tool theory and we use real Burberry music parameters and if not, what can we do deal with them to conditions.
Konstantin Eder: And chelation generalizations to extend it supersymmetry is has been studied, for instance by Saba preaching iniquity super gravity in terms of a PF theory.
Konstantin Eder: Also soda has considered this studying the algebra and I have considered this recently and some very good preparation, because they are reason resizing the dramatic approach to super gravity studying boundary theories and there are some nice.
Konstantin Eder: Some nice development.
Konstantin Eder: And also now quantifying the theory and exploiting this new and large caged up this additional landscape symmetry.
Konstantin Eder: When has to deal with the precise mathematical setting and the proper structure of this new grid along this one has and destructive habits basis on how the related to a standard conversation to quantum gravity samuels and you can draw some conclusions.
Konstantin Eder: And I personally have studied this mathematical clean way, because there are subtleties how to properly incorporates and family answer this theory.
Konstantin Eder: And essentially this beautiful mathematical structure using so called enrich categories, and this will not be part of this talk, but just want to say that there's some.
Konstantin Eder: formalism some beautiful mathematical formulas model and the theories and, of course.
Konstantin Eder: Here in this talk specifically.
Konstantin Eder: I will.
Konstantin Eder: present the classical theory as well make a to make a broad introduction, just to and explain what this all is about and.
Konstantin Eder: And, in this context that were described super gravity in terms of geometry, because this seems, this is a generic property and activate beautiful geometric structure and the theories.
Konstantin Eder: And you can extend this to.
Konstantin Eder: My channel theory says gravity theories and hire the space time dimensions and so forth.
Konstantin Eder: And eXtensible gravity's and equal form.
Konstantin Eder: And this context that will talk about the host mcdormand so it's super crowded action for arbitrary real review and preparing you for bearing music parameters sorry.
Konstantin Eder: also point out some special properties of itself to theory and, finally, I was also talking about the boundaries theory.
Konstantin Eder: And connected to the quantum theory, I was talking about properties of great connections tournaments group integration and what would they impose in context of quantum gravity.
Konstantin Eder: And finally, applications to the quantum cosmology and also someone say something about the core description, but this is the components.
Konstantin Eder: Okay, now, before I start with super gravity, I want to say something about your interpretation of gravity in terms of a cartoon geometry because it's a sad, this is a.
Konstantin Eder: If you like this can be generalized to super super gravity theory and straightforward we.
Konstantin Eder: can actually has a very beautiful structure on various.
Konstantin Eder: Various.
Konstantin Eder: theories.
Konstantin Eder: But in order to stand quiet and geometry, one has to consider first flat portal, which was the so called tension tree.
Konstantin Eder: Now phoenix plan in this famous ella ella program started the possibility to testify geometry of space, but the underlying group of symmetries.
Konstantin Eder: For instance, you could take makovsky space time and then you started your summer tour group which is given by the punk regroup.
Konstantin Eder: And then you pick a specific place time events and study subgroup of cemeteries, which was at that point, and this is given by the launch group.
Konstantin Eder: And if you don't take the caution between both groups to find this is different morphic to him, because the space.
Konstantin Eder: So the collector so the collection of space time events has the equivalent description terms of the underlying group with some trees and similar things that can do, for instance, studying the collections of space level services is also a subscription terms of course it's basis.
Konstantin Eder: So one defines a can geometry in terms of Apache ah, which is the growth potential some close up.
Konstantin Eder: With the additional requirement that the model economy because it's basis to be connected, this is just some technical requirement to just exclude exotic spaces.
Konstantin Eder: and so on, but the observation that that space time as the current description terms of account geometry.
Konstantin Eder: cartoon developed a theory which is now known as the curtain geometry studying gravity in terms of what to phone version of classroom justice gravity that performed justice gravity's at the conclusion of flipping houses.
Konstantin Eder: And you have written down the proper definition of explain this in more detail next slide.
Konstantin Eder: Just briefly so cutting down trees modeled on the clan of lead on the flat molecule tantrum T Th.
Konstantin Eder: presented by the span law P can be regardless that have some deformed version of your cookie.
Konstantin Eder: And the degree of information is included in terms of a connection, which we call a carton connection, which takes values which is defined on the default group and take a listen to the X Ray machine.
Konstantin Eder: And it says by certain properties The first one is writing variance and the second one encodes a certain sub part of your connection in terms of for cutting connection terms of provocation connection, which notes from canvas theory.
Konstantin Eder: And the third part, this is actually the most important part.
Konstantin Eder: As this leads the leads to a local identification of the tension spaces of your default group with the time space of your league which.
Konstantin Eder: Is sort of cutting condition.
Konstantin Eder: And years as an example, because this will appear at various instances, so we can consider current geometry, you know model of ages for.
Konstantin Eder: which corresponds to this can shake the tree and the digital space, and you can take your cartoon connection and now.
Konstantin Eder: You can split it by protecting on this rant and support, which gives you the lions connection Omega and also then translational support, which gives you perform E, which is the soldering form which is related to the cold frame.
Konstantin Eder: This since you have this cutting edition, the soldering from our Defense is the Marxism for me to touch on space of your manifold to the curve space time and thought to the tangent space of your flat model which has entered into the space.
Konstantin Eder: So this soldering from the it's a local notification of the flat model with the equipment.
Konstantin Eder: Now, in this constant in this context is gravity gravity terms of card in geometry, you can actually also found like actual principle defining the host actual terms of like dolman so the action.
Konstantin Eder: And this goes back to normal angelic wise and also fidelity has considered this in terms of top of the F theory.
Konstantin Eder: Now, specifically here for ages form we can we can exploit.
Konstantin Eder: property of the summit, your group, because the song Julia devices morphic to this syntactically entrepreneur and then why this edification and follows that the lines are generated in terms of MIT which expressed in terms of common interests.
Konstantin Eder: of us do this because this has a straightforward generalizations but later on for so programmed.
Konstantin Eder: So using this identification, you can define host projection of rather this quite a projection in terms of this quantity written in terms of matrices which.
Konstantin Eder: Data map map from either one three times three.
Konstantin Eder: To the popular music parameter now using this object, you can define an inner product on subjectively algebra by taking the trace and inserting this protection is quite a projection This leads to some Peter to font in a product.
Konstantin Eder: And now, if you take this cartoon connection of your theory, you can put the curvature and then formulate angles type action for taking the wedge product are which are and then computing applying the spirit we found in the product, then indeed follows that you can.
Konstantin Eder: be dependent host action, plus some additional.
Konstantin Eder: Questions so far.
Abhay Vasant Ashtekar: Everything is clear this go ahead.
Konstantin Eder: Okay, thank you.
Konstantin Eder: So this was the invitation of gravity in terms of our current show up now, this cannot be generalized straightforwardly or more or less straightforwardly to super gravity, which has mapping everything to the subcategory.
Konstantin Eder: and actually Actually, this is the starting point so coach metric approach to soccer gravity, which was initiated by an email richie.
Konstantin Eder: and develop even further by castellani to the employee.
Konstantin Eder: And this is why they actually radisson super guitar and super context, this is actually called the custom ronnie totally off the approach.
Konstantin Eder: actually find your finances and is based on dimension so get your real high academic restructuring of the theory and giving him eating reading connections to him home topic theory.
Konstantin Eder: So it's actually has a rich structures and highest dimensions, I started this.
Konstantin Eder: method rigorous manner, which incorporates and the competitive.
Konstantin Eder: inquisitive nature of me on fields, which is actually a beautiful theory using enrich categories which was intended punishment to the linear.
Konstantin Eder: And also recently has applications in the context of super confirm a few theories on remaining Superman surfaces solids by tesla your nose touch to touch money and she will.
See Tokyo.
Konstantin Eder: And this context you can describe it is it a super gravity in terms of enrich to super content geometry, which is modeled over a flat super interested in space.
Konstantin Eder: So you have now you're creating connection, which is not defined on some deformed version of your supergroup and takes values under the algebra, which is always people on the phone.
Konstantin Eder: Then you can project on even parent.
Abhay Vasant Ashtekar: Listening do you define a supergroup SOFA.
Konstantin Eder: and
Konstantin Eder: So yeah.
Abhay Vasant Ashtekar: Please, please tell us a few words.
Okay.
Konstantin Eder: Actually, this is some generic feature, if you want to actually this turns out to be a generic feature if.
Konstantin Eder: You want to incorporate ferments so and.
Konstantin Eder: actually come to the site and the context of look on look on gravity so i'm you know standard lead groups.
Konstantin Eder: Standards the groups are model over.
Konstantin Eder: To them, so in this sense the supergroup with some default version of.
Konstantin Eder: A supergroup or some group object, you can take your of manifold so a manifold locally looks like a composition of goes on some formulas.
Konstantin Eder: So we have locally this structure of a junior subspace which is generated by persona coordinates and thought creates, this is the linear model locally.
Konstantin Eder: In a standard metaphor theory just have commutative objects festival sonic confirmations now you have additional conversation with yourself and try to drive some hot part in episodic print.
Konstantin Eder: So this is the, if you like this database your local model of your default group.
Is the same.
Konstantin Eder: I just tend to his super groups which locally have which are locally model, or what is the entrepreneurs supercross which have post post persona components and for me on a component.
Konstantin Eder: So okay.
Abhay Vasant Ashtekar: yeah so we normally the algebra is explaining shifted to the group right, I mean this is the serum so here what you're saying is that you're you're telling us.
Abhay Vasant Ashtekar: The civilization, but the algebra but you're saying that somehow It can also be experiential is an object that is an advantage object it's a group, and it is it a it's not a legal right of it, what what is that thing which is course.
Konstantin Eder: It is illegal in just in general is category category.
Abhay Vasant Ashtekar: Okay, so it's a legal made the manifold replaced by the Superman.
Konstantin Eder: yeah so just consider a generalized category.
Konstantin Eder: And this category of can define morphosis and you know for my for my education and neutrality and aggression these concepts just generalized in this category and then talk, talk about have a legal so political so super ego is just a legal in this channel is content category.
Konstantin Eder: And it just isn't a classical theories local models, this is.
Can.
Konstantin Eder: You connect and share to critical.
Konstantin Eder: So now, in this context, you can split your connection terms of the evil part which gives you the spin connection Omega.
Konstantin Eder: And the processor and translational part which gives you the soldering for me and some additional feminine content by protecting your part of the algebra which goes to the feminine side, which is the spin three operators.
Konstantin Eder: And now, since you have this cartoon condition, also in the super category, and this is possible if you have some family ons properly, so you can combine this.
Konstantin Eder: This retreat field and the soldering phone to get some so called super soldering form which then leads to a local independent edification of your super manifold in terms of the local model which is super entity citizen is.
Konstantin Eder: Actually, important properties, because then you can use this object and technology to.
Konstantin Eder: Just the metric which is defined on the flat model to a metric on your manifold and this is important to define, for instance, killing US army trees and killings pinos which play and what role the context of.
Konstantin Eder: Next week, this kind of bolted on and the QA for gravity so mapping this case we call the symmetric court injunction we can map solving from a metric on your flat model metric on your.
craft space.
Konstantin Eder: Now, also in this context, you can actually explain the host action in terms of a.
Konstantin Eder: terms of a mcdonald's only type action.
Konstantin Eder: Now the host action for conquest super gravity has been considered but soda and for extended so gravity theories my code.
Konstantin Eder: And in terms of development, so the action and equal one, and it was considered barbaric on a particular question so below considering this popular music Ramat in terms of recruiting.
Konstantin Eder: and actually I want now as a full body of Christ and interpreting this in terms of some different Peter to found in a product.
Konstantin Eder: So.
Konstantin Eder: juice some variant of host protection and we can extend this in fact two to.
Konstantin Eder: Two and, in this case I will discuss to the boundaries theory, this will actually appear.
Konstantin Eder: So now, this framework, you have this selected algebra which splits into into the.
Konstantin Eder: And now, this.
Konstantin Eder: One has to structure for clifford module so guys will be having a natural.
Konstantin Eder: Natural action of your projects repeat on so far so again, the final a new project from up top but just adding this one in the odd part the state some mapping between our spend four hours people on for.
Konstantin Eder: So you could now and you in a product for taking the super trace and searching eater.
Konstantin Eder: Actually, that should happen to the emphasize this Peter is just spin one, three and variance own, this is not a very interesting all the entrepreneurs justin very none of this.
Konstantin Eder: has been months apart.
Konstantin Eder: And then you can formulate an announcement or switch we type action by taking now this super creating connection computing the curvature then fighting and are which are type action and computing and not applying this be the default in the product.
Konstantin Eder: At the end you see that this in fact it's to do find one sort of gravity with additional foundry terms, and these are additional boundary Champs effect turn out to be very important if you want to.
Konstantin Eder: Consider boundaries theories with local supersymmetry.
Abhay Vasant Ashtekar: Okay, so can you use go back one slide so in trying to define this deformed the inner product.
Abhay Vasant Ashtekar: Did you have to do some some make some choices which are kind of not canonical.
Abhay Vasant Ashtekar: What i'm trying to understand is that well is that.
Abhay Vasant Ashtekar: Normally.
Abhay Vasant Ashtekar: You know, in order to define it by very messy parameter or bad bad very bad very connection is not.
Abhay Vasant Ashtekar: Laurens advantage right, it is something that might require some additional structure, so what happened here what structure you to use, which is additional.
Konstantin Eder: So concerning from the Meta concerning this.
Konstantin Eder: This transition from ordinary gravity to so description of recording Eric reverie terms of our host action to super gravity you actually don't make any choice so you're just apply this be beaten additionally on as our.
Konstantin Eder: And that's it so you're just now compute the curtain curtain.
Konstantin Eder: Of this new connection, which is the curtain connection of this.
office.
Konstantin Eder: Space model and then you apply this in a product with as additional data and then everything cancers nicely, and you really end up with your.
Konstantin Eder: host action also prepare.
Abhay Vasant Ashtekar: For example, this the connection, he does not know anything about.
Abhay Vasant Ashtekar: can only go to the composition of the Lawrence group into into.
Abhay Vasant Ashtekar: into boost part in the.
Abhay Vasant Ashtekar: rotation part or a family absurdity compositions it does not know anything of that, but the barbaric connection finally.
Does.
Abhay Vasant Ashtekar: So, how does in super gravity framework that information trickle down, so I thought must have been in the in the inner part of beta.
Okay.
Konstantin Eder: So this is actually called during only principle.
Konstantin Eder: So i'm, this is actually what all this theory of the critical part actually is about so.
Konstantin Eder: Your fields.
Konstantin Eder: Genetically defined on this whole.
Konstantin Eder: New space and super manifold and just in your space, the manifold is embedded in this metaphor.
Konstantin Eder: And then, as the principal and you can actually prove this principle Pacific cases that.
Konstantin Eder: If you this is actually applied awesome can context of super control theories.
Konstantin Eder: and proven rigorously So if you define your connection if you require certain properties which is actually concerning the pullback of your connection and certain direction the direction so if you manifold then this if you.
Konstantin Eder: To the underlying specimen for them, if you acquire this is, if you just recorded this property, so your your connection is uniquely classified in terms of the public of curvature and the torsion contribution.
Konstantin Eder: To the underlying space, the manifold and yeah so everything is encoded on your space command from.
Konstantin Eder: This is the soccer very annoying principle, and so, because you can prove this.
Abhay Vasant Ashtekar: But actually you're saying that whatever extra information that I need to.
Abhay Vasant Ashtekar: construct a barbarian connection is really or others in the space time level once I give you a spacetime level that this principle push it to the.
Abhay Vasant Ashtekar: To the supermarket level yeah.
Konstantin Eder: So manually it's quite it's mainly it's encoded and completely on space time and phone and some odd parts and you can shift a little bit on the odd part of human thought, and this is actually what you call a supersymmetry.
Abhay Vasant Ashtekar: What you're saying is.
Abhay Vasant Ashtekar: Am I correct, that is a statement can it be said, by saying that Well, yes ordinarily in ordinary gravity not super gravity to introduce our very busy parameter or a Boxer barbaric connection I need some.
Abhay Vasant Ashtekar: Non covariance sort of city composition of the connection.
Abhay Vasant Ashtekar: And so you're saying that once I do that then his promotion to super gravity is an ambiguous is that what you're saying.
Konstantin Eder: yeah okay.
Konstantin Eder: The next one, your space, the manifold supersymmetry by the summer symmetry extra photos from the action itself.
Konstantin Eder: Thank you, both things and culture connection really.
Konstantin Eder: Are there any other questions.
Konstantin Eder: Okay, so so far, this was super gravity.
Konstantin Eder: You know now we have formulated the sexual principle, and now the question what is actually the underlying supersymmetry in this theory and then the canonical theory, what is this was a constraint.
Konstantin Eder: OK now let's do we have we actually talked about this now and to really approach they treat supersymmetry in terms of submitting Marty Marty systems.
Konstantin Eder: Because you have no you're not part in your manifold you can try and simply procure connection if you transform it in the odd part.
Konstantin Eder: and translated in the odd part of your manifold this is quite a super different Marxism and this is actually what supersymmetry is so you slightly different in the hard part.
Konstantin Eder: You fill out the form of space time sensitive form and the odd part, and this is if the action is invariant under this one is because the supersymmetry.
Konstantin Eder: This is what's a dramatic approach try songs in this framework.
Konstantin Eder: And now, and it's cut into reggie Kramer, particularly if you consider a new one, you can use the correspondence between the curtain connections and address my connections on associated bundles.
Konstantin Eder: So curtain connections can be mapped in one to one correspondence to else my connections on associated bundles where else phone connections are the standard connections to use in English, he was.
Konstantin Eder: Why this correspondence that follows that.
Konstantin Eder: You have a large symmetry just given by a supergroup and so you can study in our new class of locates transformations which locations masons which along the odd part of your group.
Konstantin Eder: And if you study this type of obligates transformations It follows that.
Konstantin Eder: swamp component components of your connection and your service and your action, this is really a symmetry of your theory provided Omega satisfies it's really questions.
Konstantin Eder: So supersymmetry in this context has the interpretation terms of gauge cemetery not direction of your fuel generalized age group in the 1.5 water formalism so provided Omega six by 650 questions.
Konstantin Eder: But since you have supposed to impose this constraint lacombe symmetry is not a proper transmission so could fit depending submission.
Konstantin Eder: And in the canonical theory any local subservient uses a constraint so on the canonical theory and additional constraint, which is the socket susie constraint.
Konstantin Eder: And it's a generic generic feature, because we have this passion, the petitioners of okay symmetry can the commentator between.
Konstantin Eder: generated generators cool generates time translations and spatial transformations and Lawrence transformations.
Konstantin Eder: So generically you can expect an economic theory that this was the constraints, the quantitative will give you the hamiltonian constraint and some additional kinematic constraints, such as the currency constraint, or the.
Konstantin Eder: Marshal constraint.
Konstantin Eder: And this is a 50 penetration summation who loves functional genetically also fit dependent.
Konstantin Eder: yeah and, since you have this relationship relation between susie constraints hamiltonian constraints, was that this constraint is superior and economic performance and to me Tony constraint, because once you solve this constraint, this is a solution of the time, but not vice versa.
Konstantin Eder: So this is the canonical theory of this object is extra central importance to study the dynamics of the theory.
Konstantin Eder: And we have done this in the fourth theory for amateur real music parameters.
Konstantin Eder: And this is just one part of this constraint extra get five other terms and 16 very complicated object.
Konstantin Eder: And so I just picked this one, because this should be related to the curvature contribution of your hamiltonian constraint and the classical on the theory.
Konstantin Eder: Because application of credit derivatives and self gives curvature, so this is an interesting subject to find relations to the conversation of courage and a standard quantum gravity.
Konstantin Eder: A Beatles album is the aspect of our connection and five cherries now somehow half sensitized to registering of it.
Konstantin Eder: Now we have quantities objects and actually that exists, we responsibilities sushil but be a matter of the simplest possible form so because.
Konstantin Eder: yeah this was possible farm and also you want to watch it K terms, because these are involved too much proposal.
Konstantin Eder: To or the integration part of him 20 constraint, which you should not use at this stage, because actually want to find a consistent, in addition to the conversation of Tony constraint.
Konstantin Eder: And this context we have used to support various more than one well it's more than one operator, because this was possible in this case, because this operators different structure in the.
Konstantin Eder: sense hamiltonian constraint, but we also apply to every also standard possibility to your staff to can understand and we found this operators well defined and finite.
Konstantin Eder: This is some some generic action of this first part of the constraint.
Konstantin Eder: So what it does it generates from yawns on the vertex, but it also lends itself to the action of on one particular spin advantage it's been a good read text regenerates registries.
Konstantin Eder: And a couple of strong capital firms and the truth is property if it's too, I strongly coupling between farmyard some gravity and this is what to expect for chenab solutions of supersymmetry constraints, so you.
Konstantin Eder: expect really that this constraint has supersymmetric solutions containing both Poles on some friends.
Konstantin Eder: So this was just the conversation with this was a constraint and.
Konstantin Eder: Now it's a generic property of the oddest constraints and economic theory that they are very complicated and supersymmetric theory.
Konstantin Eder: And the canonical theory that this seems to be that down the structure of the theory is actually completely uninformed realism.
Konstantin Eder: So one would like to find a way to partial restore this dramatic structure one finance and therefore theory in the covariance theory.
Konstantin Eder: and actually this turns out to be possible in the car theory.
Konstantin Eder: Because, in this case, if you choose better to be minus I and follows this host protection now becomes a proper protection on a sub graph, of course, be one for.
Konstantin Eder: Images map to ti plus and cloth map to QA.
Konstantin Eder: which has some component of your honest opinion.
Konstantin Eder: And you studied the properties of the search bar scene status from the process of algebra which, in case of anonymous information because most constant is getting my auto selecting either pro.
Konstantin Eder: Or the article to super hungry okay so far and nomination and case of industry cosmos constantly.
Konstantin Eder: Trying to do this, property that is the now really maps to a proper setup algebra and follows that you're swimming super host mcdormand so the action.
Konstantin Eder: Now really has a always P one to invariance trace so really you have manifested always people want to see kitchen variants in this theory.
Konstantin Eder: So supersymmetry, which already has the passion to potential in terms of gauge cemetery products using some constraints now becomes a true cage symmetry even option.
Konstantin Eder: And this was the observation affiliate based on the algebra and study microbiome click on bullying smaller.
Konstantin Eder: Now, using this kind of protection they can apply this to your card in connection and then this gives you a Masonic part which is the self to ask the connection and Carol exceptional opponents of the description field.
Konstantin Eder: Now you can study the properties of connection the so called a journalist to procreating connection and using now this correspondence between the coach and connections and.
Konstantin Eder: Most cage fields this industry now a cage field really on the assessment So in this sense, your theory now really becomes a super young this case theory.
Konstantin Eder: So partially in the current framework supersymmetry now concept true case.
Abhay Vasant Ashtekar: But, of course, is only gonna magically this super young misty right because there's no background metric here, whereas young is super young this theory that the background metric.
Konstantin Eder: Is.
Abhay Vasant Ashtekar: The likelihood is complete.
Abhay Vasant Ashtekar: The dynamics competitive, is this the tedious two different models of Kobe elegant, whereas the young man Superman he said he's not he doesn't go read it so it's only the kinematics level that is like super St.
Konstantin Eder: Louis.
yeah.
Hanno Sahlmann: The other half of the supersymmetry now sits in in in in some supersymmetry constraint and that will be very different from what you have in.
Konstantin Eder: Now, the question arises is this generic feature it's just a political leverage of the one case.
Konstantin Eder: Now you can study the Cairo Cairo part of your algebra and you actually see that this some generic property of your generic code or property of your algebra.
Konstantin Eder: And this also forms and supply Japan case of extended supersymmetry so you can fall out your connection also extended to the cemeteries.
Konstantin Eder: Although at this stage that does not mean that your theory really will have the symmetry and kids have extended source of truth, but it just means.
Konstantin Eder: That this may be n g to also engage symmetry for particularly for hire some supersymmetric theories and 22 we can really prove that this is the case.
Konstantin Eder: And also can ask the question does this allow really popular music parameters and the answer is no, because now, you have to include both components of your piano family on to a.
Konstantin Eder: To Alpha and then since this both different kind of components now generate momentum and pick a time and momentum is encoded in terms of the door electric field.
Konstantin Eder: You can definitely say say this doesn't have a purpose of algebra and just not possible tourists top some part of the supercharged mentors have a pitch symmetry.
Abhay Vasant Ashtekar: But you could have walked in the in the reminder signature break down the whole.
Abhay Vasant Ashtekar: The whole super gravity considerations are valued in the mind and signature as well.
Abhay Vasant Ashtekar: And kilo.
Abhay Vasant Ashtekar: you're answering the reminding signature, but this should be possible right, I mean the real data is also a big data can be equal to one plus or minus one.
Abhay Vasant Ashtekar: I lorenzen signature, I completely agree with what he said, but it seemed to me that, although you know what for good reasons, you did not emphasize that one can also do the all this in the Romanian signature if he didn't do that then.
Abhay Vasant Ashtekar: Then I think one can just use the beta.
Abhay Vasant Ashtekar: You can say something we should just be efficient, say, anybody who wants to say.
Hanno Sahlmann: Okay, I believe there will be.
Hanno Sahlmann: There will be some obstruction, because it seems that in equal to one.
Hanno Sahlmann: super gravity in the acadian signature somehow doesn't doesn't exist.
Hanno Sahlmann: Nice, and so, but, but what you could do is.
Hanno Sahlmann: As far as I understand we manian signature for n equal to, there is a theory there that's well defined but it's a complicated subject because you can also ask what what happens if you do.
Hanno Sahlmann: A week rotation to I mean to a to a normal supersymmetric theory to a week rotation, then there should be some kind of theory so maybe something is possible, but it is not straightforward, at least not with an equal to one, as I understand.
Abhay Vasant Ashtekar: It Thank you.
Konstantin Eder: So this is some popularity of the theory.
Konstantin Eder: So a plus can be used as an actual candidate to contest gravity.
Konstantin Eder: gravity.
Konstantin Eder: And, by its very definition, it contains both gravity Meta degrees of freedom message to identify description of partners have more fundamental way of contact Informations in this approach.
Konstantin Eder: And, of course, because now you have really some part of this surgery absolutely true gauge symmetry the substance substantially simplifies your constraints and also partially SOS SOS them why engagement variants.
Konstantin Eder: Actually, and context of glucose there's also times that seems to be a natural candidate to study in the boundaries and from a glucose gravity, in particular, to define PBS dates and can be used for like hosted counting.
Konstantin Eder: And then this can also be used, maybe to draw conclusions on relations to description upon the theories and string theory, I will explain this in more detail later.
Konstantin Eder: So now we have considered the quantum theory, I will just say something very briefly about this summary So what do you need for the quantum theory need a lot of me is really terrible spaces and we need to spend network basis.
Konstantin Eder: And for a lot of me, such as what to say that this actually has a very rich structure and studied this and rigorous manner and actually turns out this quantization of glucose gravity on groups actually is well adapted to this enrich category petition of of manifolds this is some.
Konstantin Eder: Generic structure of such a great anonymous we have a standard persona economy given by the one we have as a faster connection and some power of public transport, it for me on alone edge.
Konstantin Eder: And this is some you can think of this, this is a mapping to a group, and this, so you can think of as the configuration space concluding both post on some familiar configurations.
Konstantin Eder: And then later of your contacts in terms of groups this works very nicely.
Konstantin Eder: So in this framework, it follows the grades Hello miss you too one dimensional expectations of maintain geometry and finance apparently transport a long pause on economy.
Konstantin Eder: And so Meta geometry is encoded along these lines.
Konstantin Eder: Actually, if you now want to construct in a product on your space, you have to pick a mesh on your of illegal, and this leads to a crime structure, a little bit space.
Konstantin Eder: And in fact this is related to a standard equalization look on gravity, although this may seem a bit hotter the market, the beginning just want to explain why this actually it's also used to groupon gravity.
Konstantin Eder: For instance, if you take your, so this is actually what is the manifold is so you can take this as a discrete super manifold you have your spin network, as has been network state.
Konstantin Eder: And you have a very antiquated the vertices.
Konstantin Eder: And these words, it is registered as you know you have these fibers are where your sonic manifold so you can describe the difference in terms of these clouds here which, if you so men construct also for vertex.
Konstantin Eder: redrawn.
Konstantin Eder: At the Center you have this.
Konstantin Eder: This family on sitting now if you consider the vector space of the functions defined on this rejects, you can describe this equivalent in terms of functions on a supergroup.
Konstantin Eder: By taking G as Su to take to the power of number of edges incident at this rhetorics times some particular space, which is soccer the super point to each red X have a super point.
Konstantin Eder: And if you study now these functions on this group, this is a given by the 10s of product of it.
Konstantin Eder: Instead, they try to function so two.
Konstantin Eder: Times functions on this.
Konstantin Eder: On this.
Konstantin Eder: The Superman for this super point to call it, and this is as a morphic to the and anti symmetric crawl space.
Konstantin Eder: So you actually get your standard functions on the vertex Now you can start again transformation in terms of regular rotation so functions on this group, this is extra standard action on the supergroup.
Konstantin Eder: And you can use reconstructing measures, you can use asked misha, which in this case it's given by how much of so two times two pairs and integral.
Konstantin Eder: So now you're making a transition to as you choose.
Abhay Vasant Ashtekar: So it's no longer settle connections.
Konstantin Eder: Now this is just.
Konstantin Eder: To point out relation to standard, I could have.
Konstantin Eder: Okay it's about gravity using this this greater grammys you actually encode from your too long edges, which is somewhat encoded in terms of supersymmetry which summer requires the gravity and pheromones are treated equally in terms of their belongings their terms of string like expectations.
Konstantin Eder: This is just to draw conclusions that the structure you observe there is so much structures, you have such integrity.
Muxin Han: Since, since you democratize this space, and so, is it going to cost a nominee it probably breaks as soon as breaks your she was imagery right because, up to the sweetness of the of the server space.
Konstantin Eder: No.
Konstantin Eder: So, in case of.
Konstantin Eder: Do you mean on the supersymmetric context.
Muxin Han: yeah yeah i'm if you're introduced a disk space, I will assume that it will cause some anomaly.
Muxin Han: which may break supersymmetry.
Konstantin Eder: Concerning this one part of your symmetries his riches in this context really imposed in terms of catering stasis restored.
Konstantin Eder: The white right supersymmetry.
Konstantin Eder: So if you have two parts of some switches left to switch which is, which is a corporate and the theory straightforwardly and we have additional symmetry the left at the supersymmetry remaining in your theory, which is the right system to call it.
Konstantin Eder: And who is causing the homie in theory.
Muxin Han: But usually supersymmetry is is like a continuous rotation we're cutting us transformation down the young are super space or I sum up with them up superset and and since your disciplines hyperspace them probably you break some supersymmetry right.
Hanno Sahlmann: yeah I think it's the same question as as whether we have an anomaly, with the hamiltonian constraint, when we quite.
Hanno Sahlmann: A complicated question, and it would have to be looked at in detail what yeah what it constantly just wanted to say is that, in this formalism at least half your supersymmetry is protected it's going to be implemented, but there is another half that you have to take care of.
Muxin Han: OK OK, I see.
Abhay Vasant Ashtekar: You could.
Abhay Vasant Ashtekar: Use you know all possible graphs right and and worry about cylindrical consistency and just take the project, the limits on that would that not be real possibility.
Abhay Vasant Ashtekar: So in that case I mean we don't expect any.
Abhay Vasant Ashtekar: This is there any problems with the different models and environment so similarly year what melodic.
Abhay Vasant Ashtekar: expert, the problem with the supersymmetry badness I don't know I mean i'm just trying to say that.
Abhay Vasant Ashtekar: You don't have to reject discrete ization.
Hanno Sahlmann: Exactly I buy that would be the end goal now since, since this is the self tool theory one has a problem with non compact directions and so on, and then it's not straightforward to have this this measure on a bar.
Abhay Vasant Ashtekar: or something like this, but.
Hanno Sahlmann: In principle, that would be the idea to not not to.
Hanno Sahlmann: Not to lattice gauge theory approach, but really have floating lettuce.
wolfgang wieland: Maybe, just a quick question.
wolfgang wieland: So in this lead is this.
wolfgang wieland: This presentation of the Community, so the superpower, of the of the connection to this family once they see it now should, I think of them as sitting on the link or at the end points of the link and if they see that the endpoints are they related by constraint.
Konstantin Eder: yeah actually it's in between also.
Konstantin Eder: So it's really a term transplanted along your edge.
Konstantin Eder: This is what you what this one was actually telling you so.
Konstantin Eder: You have to present economy and the additional it's very on which is religions brought it from the beginning to the ending of your life of your edge so it's really content along the search string like expectation.
Konstantin Eder: But if you consider transformations that really transforms on the left and the right hand.
Konstantin Eder: So it transforms on both answer but it's localized along the stage.
Hanno Sahlmann: Yes, it is a component of the connection so when you form a hold on me, it will be all over the edge.
Hanno Sahlmann: And then it's a weird question to even see how you build something up that transforms correctly, but Constantine made the calculation and this this sort of the result if you want to pry it apart, again, then you see that there are lots of Masonic holanda means that.
Hanno Sahlmann: move back and forth these formulas all over the all over.
wolfgang wieland: it's a giant.
Hanno Sahlmann: Yes.
Konstantin Eder: Actually, this is just.
Konstantin Eder: Reference the standard action.
Konstantin Eder: This.
Konstantin Eder: Defining action officer to see on this co feminine.
Konstantin Eder: is given by the Atlantic.
Konstantin Eder: And now, they can study properties of favorites basis and you see actually This gives you structure which you also find in standard to quantum gravity standing variants.
Konstantin Eder: Because you have this Superman for interpretation of it's been entrusted with finance and you will study measures they're separate spaces you catch this the product has been by the standard so when a product and some verisign integration and definite and a product.
Konstantin Eder: Please practice.
Konstantin Eder: Now you have actually the canonical during post reading conditions also confirm yawns because the Code of Conduct conduct mentors as.
Konstantin Eder: As the conjugate of the of the of the very odd and this uniquely fixes you and so called crank completion, so this is just this choice of a particular measure to Paris intensity such to this measure is positive, different so this day is today the product is proposed.
Konstantin Eder: Actually, the same same happens now and.
Konstantin Eder: So brokerage context also now you have the interpretation in terms of parents along edges not sitting at the vertex which is some property of supersymmetry.
Konstantin Eder: yeah so partially.
Konstantin Eder: Restricting positive definite ness of your craft spaces is sloughing heretical justin's of your family, but you still have to solve the repetitions of the complex have two variables might have to grow, and this is still an open issue of course and.
Konstantin Eder: In classical sonic theory and therefore have three seems to adapt formalism because we can restore some of the cemetery so we have considered a particular similar to just model.
Konstantin Eder: Which is based on the model study by teeth X and talking octagon.
Konstantin Eder: and which is based on the hybrid homogeneous as a trophy concerts with a Masonic confirming Ionic degrees of freedom.
Konstantin Eder: And, in general, finance on a compatible, because I sort of pre but now this context, because you feminine is part of a connection and, in particular, in the current approach we have noticed in large cage symmetry.
Konstantin Eder: Actually follows that you can use this exploit this and large trade symmetry to get non trivial semiotic degrees of freedom on your machines as a topic.
Konstantin Eder: Based on the phone.
Konstantin Eder: So what we have done, we have studied, which is as a topic and super connections and, in fact, it follows that, in this context explosion is not sketch symmetry.
Konstantin Eder: That you get the connection, which takes this forum, which is actually very funny conversions are those as post buddies in this context that follows from from this isn't large kitchen.
Konstantin Eder: Where now see it so some complex Gala course some complex number, corresponding to the tropics connection.
Konstantin Eder: and say is the feminine conclusions.
Konstantin Eder: And also can show that is actually the merchant answers you can study, which is consistent with the episodic relative conditions because see is as a topic and then.
Konstantin Eder: To control tends to also has to be as a topic and it's actually the most to dance with me on can have to get restored, so to speak.
Konstantin Eder: So and it's very good follows that.
Konstantin Eder: You have your connection to mental P, and the family and conclusions a few freemium say anything to mental pay, which is why this created consolidations.
Konstantin Eder: and your physical constraints, you have some pseudo cost constraints, because some cows symmetry is still restored in theory, they have to solve it later on.
Konstantin Eder: And also have not dynamic constraints that given by the left's and rights what's the constraint and the hamiltonian constraint.
Konstantin Eder: And then you can study the constraint it right actually we have very specific choice of the parity.
Konstantin Eder: And this particular choice of the parity, you can find that this algebra and it closes and if you then returning constraint and Christian right so as a constraint and this structure coefficients on dependent.
Konstantin Eder: And you definitely have relative conditions.
Konstantin Eder: For the Masonic connection where K is the space curvature to zero or one, and this is not a continual contribution, which is as a topic.
Konstantin Eder: And you have additional recognitions for your family.
Konstantin Eder: So we now use this super enemy in order construct the state's bit of the theory computing this along the along producer cell.
Konstantin Eder: has long straight edges of the features of cell and it follows, and in this case we drive the credit flux algebra were a not can quote the economies in a one output contributions, which are the variants.
Konstantin Eder: And then, for the quantum theory, we started the corner this tension of this entrepreneur creditor but space so it's great instructors all come naturally in this framework, but.
Konstantin Eder: Because we treat this equally.
Konstantin Eder: And the quantum theory, then you end up with this kind of hybrid space so http This is because this the.
Konstantin Eder: This director space of almost predict function so almost almost periodic calm have a conscience and complex plane, which was from him first time.
Konstantin Eder: introduced by wasn't doing.
Konstantin Eder: So this vector space is generated by these types of functions, we R E to the museum use some real number takes values and the complex application of your one, so you can regardless in terms of channelized characters with the complex plane.
Konstantin Eder: and actually can also study, whether this can define define the terms of functions of the group and we've done this it's so cold for every entrepreneur as a function of the entrepreneur, which has the coop structure, but not with us to watch to watch the group.
Konstantin Eder: But tractor you just get this far, we have this notion of choice to not only each of them, you see reset and feminine williamson's.
Konstantin Eder: And then we have also impose ready conditions they were used to have.
Konstantin Eder: tentative semiotic fields and actually this drastically simplified you the relative conditions.
Konstantin Eder: And we found that these candidates and soft exactly and the in particular shows you a unique and a product which in this case translate to peter's to Krishna.
Konstantin Eder: And also have contrast the constraints, so this is the form of their rights, was the constraint, where we follow this symmetric ordering proposed for my team Benito mountain or middle.
Konstantin Eder: So i'm N, plus a Lambda, and this is this quantum area which, which is, which should be imposed from the food theory and plus minus is.
Konstantin Eder: The connection which approximate by anonymous data is some semiotics symmetric order for me only contribution which actually comes from the trials of have tentative seminal.
Konstantin Eder: Companies are using these constraints.
Hanno Sahlmann: Are you ready interrupt you.
Konstantin Eder: But.
Hanno Sahlmann: I worry about the time yeah I think if you could try to highlight the just give the highlights.
Hanno Sahlmann: And then finish, and if you guys have questions about the details of the constraints or whatever we are happy to answer that maybe consulting should get through the, the most important bits in the next five minutes or so that we can go.
Konstantin Eder: So we completed the autograph and what we found is.
Hanno Sahlmann: Perfect matching to the.
Konstantin Eder: concert concert concert entrepreneurs who the constraint address give me 20 constraint right, so the constraint is the same coefficients.
Konstantin Eder: and also to make this.
Konstantin Eder: make this happen, we have chosen symmetric ordering and.
Konstantin Eder: Then we have also considered the semi classical limit of the theory for making this generic concerts with.
Konstantin Eder: Some continuous functions to find positive sector of the volume and then taking semi classical limits, but assuming the quantum corrections haha.
Konstantin Eder: unimpeachable we find the generic solutions of this constraint now contain unlocking state which is this performance proposed but it's using standard mini super specific needs.
Konstantin Eder: OK, now we actually want to also consider the food and remix, and this is actually a bit harder problem is supersymmetric is because it cannot just had a simple as get a fetus relational clock because.
Konstantin Eder: dynamics are governed by susie constraints, so you have to add Meta fields which are locally supersymmetric so that such that they contribute to your sushi constraint, and so this actually has to be extended to these type of mentor, which is actually.
Konstantin Eder: Which is actually harder task in this report.
Konstantin Eder: working on this.
Konstantin Eder: And also, in this case actually you you observe simplification, because they have any constraints generic to quite a positive difference and so to constrain just give them as credit with the hamiltonian constraints, so this simplifies the dynamics.
Konstantin Eder: And also, we would like to better understand the paradigm in theory, we have made a parity choice which is consistent, the constructor but still would like to call corporate.
Konstantin Eder: has substantially down into cosmology recommends.
Konstantin Eder: And now we are studying boundary theories and actually a true to this hosts with donovan Zulia interpretation of the super gravity action you get naturally in the boundaries.
Konstantin Eder: And this is some new development and the dramatic approach that these are, in fact, those contributions have to consider if you study in our boundaries and supersymmetric series.
Konstantin Eder: So, and even our study self do theories and follows that this boundary serious infections, to question Simon theory, where the boundary.
Konstantin Eder: Consignments every this super, the Group of the time series, in fact, the supergroup This follows from from sephora theory and soft generic property in each metric approach to the city.
Konstantin Eder: And Actually, this was not that hard topic at the quarterback in the past, but now there are some observations in string theory.
Konstantin Eder: That are considered Pacific string collaborations on the brains that effect, observe social science theories with supergroup so each group, and this is now why actually.
Konstantin Eder: This type of theories on fact interesting interesting and you can actually draw a lot of conclusions out of it, for instance, because the sketch demetrius or not, but also complex age groups, as we observe.
Konstantin Eder: And look quantum gravity and so you can use this to get better idea how to describe ponder theories and practical coupon credit, and we are recording this.
Konstantin Eder: So we started supersymmetry in this context of the traditional supersymmetry in terms of gauge cemetery the garden traumatic traumatic using self to self serve that this is real true cage symmetry of your steering.
Konstantin Eder: It started the mathematical foundations of the theories using so called rich to protect your categories.
Konstantin Eder: Reading some deconstruction the theory, there was a bunch of the quantum theory contest susie constraint, or whatever real music parameters study properties of this constraint.
Konstantin Eder: Is a consultative study the alarm is dropping similarities to stand up a Gucci.
Konstantin Eder: supergroup interpretation, then we also practice to symmetry just models and cosmology and there we found a problem to have in the future, we can preserve consistently and maybe this gives us, it gives us hope that this may be possible in the company theory.
Konstantin Eder: And not look if you consider the full dynamics of the theory, we consider in our boundaries in the theory and maybe make contact true description of parties here's the context.
Thank you.
Abhay Vasant Ashtekar: yeah I got a couple of questions, so the what the process would be.
Abhay Vasant Ashtekar: and
Abhay Vasant Ashtekar: This quarter cosmology that you did we just so.
Abhay Vasant Ashtekar: Here, the only mcafee you had what the the the the spinner field, so if I did not mean in Masonic sector, I would not have a spin a field and then just will be.
Abhay Vasant Ashtekar: Negative or small logical construct rizzoli and then lonely there will be only one state of the be this one pattern of family up states as a solution to the constraints.
Abhay Vasant Ashtekar: So my question here is that in that case we there's still a question about you know what factor or you're using and song.
Abhay Vasant Ashtekar: And is the fact that you have here, for example in the as potential the bows onyx sector, what does it correspond to which quantization schemes this correspond to is it called supposed to be bar minotaur are completely different on.
Konstantin Eder: This contract, we refuse to move our schemas.
Abhay Vasant Ashtekar: It okay so because of its volume that's me Okay, then the next question was really I mean it's not possible to use the somehow the spinner feelers o'clock.
Konstantin Eder: yeah the problem so.
Konstantin Eder: classically it's you have this and the competitive nature of his family on.
Konstantin Eder: writing the first man values quantities.
Konstantin Eder: and
Konstantin Eder: So they don't have to call this a valid the body of such a such a quantity, so the body is the classical real number underline this question read it fit and this is trivial in case of permanence.
Konstantin Eder: Right so.
Konstantin Eder: Even in the classical theory.
Konstantin Eder: does not make sense to speak about.
Konstantin Eder: Everything I was just wondering if you could not.
Abhay Vasant Ashtekar: combine the two meals and Cooper pay or something like that and not have.
Konstantin Eder: Any quantities.
Konstantin Eder: And they appear.
Abhay Vasant Ashtekar: Okay, the other question was the biggest simple one, which is really that if I think of the connection normally I think connection is having you know physical dimension of one upon length and when you say that the connection has one part which is.
Abhay Vasant Ashtekar: Omega, which is the connection as one part is Omega is also connection that, as an image, or one of our lead, but then the other part, is supposed to be a.
Abhay Vasant Ashtekar: frame and a spinner fee and they're completely different physical dimensions so so if y'all cosmological costume, then you could use that in order to say that well you by e really mean he divided by l one l is the length parameter.
Abhay Vasant Ashtekar: But it, but in the without the cost was constant How does that make sense of this as a parts of connection because physically they're quite different quantities.
Abhay Vasant Ashtekar: I mean.
Abhay Vasant Ashtekar: Not not not the full theory, not in the cemetery production, this is really the full theory, the connection is supposed to be a supposed to be, you know, has two parts one is he what is sigh and one is Omega.
Konstantin Eder: yeah.
Abhay Vasant Ashtekar: So I understand mathematical was happening, but physically, how do you reconcile it would be with the fact that.
Abhay Vasant Ashtekar: That Omega and and a half dimensions one upon lenticular physically because I connections, where is he, in this case will be dimension less and the formula has some other dimensions So how do you put them together.
Abhay Vasant Ashtekar: In other words, there's a mathematical fee, but that is not read the frame fear, because the same feel as different physical dimensions.
Konstantin Eder: So now.
Abhay Vasant Ashtekar: There must be some.
Abhay Vasant Ashtekar: Some constants relating the mathematical fee with the frame philly and similarly mathematical field side with the physical form bionic field side you know.
and
Konstantin Eder: Also in this context to see it.
Konstantin Eder: listed here, so no paper, this time, and so, yes, some are not included because there's different dimensions and the.
Abhay Vasant Ashtekar: season so putting a Las Vegas places, but then.
Abhay Vasant Ashtekar: That space limit yeah.
Abhay Vasant Ashtekar: So I mean in the Flash space limit that just doesn't work that.
Konstantin Eder: out now there's, no, no, no, this is this producer or not at.
Abhay Vasant Ashtekar: All I say yeah but, but in the filter you can add additional judicial a lot, so you will not be able to.
Konstantin Eder: Now the.
Hanno Sahlmann: Question wasn't simple question and i'm stumped so I we we think about this, and we will, that is a resolution to this, but I know i'm.
Konstantin Eder: not seeing it so we're really missing out not.
Konstantin Eder: yeah right.
Abhay Vasant Ashtekar: But, but in the full theory we don't have and the last question was about to the dental community that i'm puzzled by something else on the one hand we all say.
Abhay Vasant Ashtekar: That well with the cellular connections, you know we don't know what to do, because it is a non combat group, and so on, but it's been forced people routinely deal with the non combat groups, and you know, using representation theory of hustle.
Abhay Vasant Ashtekar: So to see and.
Abhay Vasant Ashtekar: so little bit not clear about here, it seems to me that there's some tension here which i'm maybe that people like low and ascii or.
Abhay Vasant Ashtekar: Mathematical people they might you know both spin forms and and canonical gravity they might perhaps explain to me why we cannot use the techniques that are used in spin forms, you know the representation theory of the.
Abhay Vasant Ashtekar: For the full audience group.
simone: When we don't require the objective limit usually so the fact that there is no ceiling legal consistency in the standard sense let's see it's not a stumbling block for us.
simone: But but but.
Abhay Vasant Ashtekar: But even given graph or a given punk a fertility for like a finite number of degrees of freedom you don't know how to measure because the group is non combat.
simone: I.
Abhay Vasant Ashtekar: know.
Our major.
Abhay Vasant Ashtekar: I mean hot don't have normalized heartbeats.
Abhay Vasant Ashtekar: Right, so that but, but you still do this calculation so, then what i'm trying to say is that are we having.
Abhay Vasant Ashtekar: Very.
Abhay Vasant Ashtekar: different standards.
Abhay Vasant Ashtekar: They believe that we are happy with what's important people do i've not i've not using our normalized our major and then also not wedding elicited consistency, then, why cannot handle and.
Abhay Vasant Ashtekar: and constant didn't do the same thing in super diversity just looking at some finite.
Abhay Vasant Ashtekar: Fixed black, is it for life.
Abhay Vasant Ashtekar: And he said to.
Hanno Sahlmann: me, I think, to a certain extent that's that's That would be my whole like, for example, thinking about the black holes.
Hanno Sahlmann: Maybe one quick make a calculation in the in the normal real theory without knowing about the consistency conditions in the park and so on, just knowing knowing.
Hanno Sahlmann: Knowing a little bit about accuracy so for certain products, it might not be so so necessary or for whatever the spectrum of the area operator, or something like this, this might be might not be so might representation theory might be enough.
wolfgang wieland: of perhaps.
wolfgang wieland: Perhaps it has to do, then, with the reality conditions, because if we set gamma to I we really work in a complex theory and wave functions are supposed to be a morphic and then, then the homage in a product on a cell to see.
wolfgang wieland: doesn't give enough product for for an elliptic re functions, and I would suspect that maybe a similar argument, then also holds in super gravity, so I think that's kind of the, the reason why, in spin forms we work with.
wolfgang wieland: integrals on non compact groups, because after all the bay function is not an amorphous plan in the canonical theory setting gamma to I gives us to would really lead us to a morphic.
And then it's not keyboardist.
Abhay Vasant Ashtekar: So, or maybe disciples understand what you're saying that in the cell phone case the boundary theory one is still using a Su two connections and the boundary here, but the stage that what he's looking at the boundary that still all normalized because he two connections.
Abhay Vasant Ashtekar: yeah is that what is that.
simone: Both for both gamma imaginary but also real right wolf can give it agree.
wolfgang wieland: Where I would say you don't really have a spring from theory we've come a quilt why.
simone: Okay, fair enough.
Abhay Vasant Ashtekar: yeah.
Well yeah.
simone: he's always thinking of respect to issue yes.
Abhay Vasant Ashtekar: yeah, the problem is always taking this book as you do, and then the statement is that it is really the the representations you're using and so on with this is to see how to do with the.
Abhay Vasant Ashtekar: In between, not the boundary state but, but the bulk the the spin yeah Okay, I think that that's that's that's fair.
Hanno Sahlmann: yeah Let me add that another huge huge student of mine is working on precisely this problem of implementing the reality conditions, and it seems that, at least when one of them is really hard but.
Hanno Sahlmann: But it seems the natural thing is really that you start with Hello morphic functions on so to see and then.
Hanno Sahlmann: Imposing some part of the reality conditions brings you down hopefully to something like as him to again and then also this this problem might might disappear.
Abhay Vasant Ashtekar: As they've been working with transform I mean I this was what I was asking co you said fine equal to one some other is an obstruction that you cannot really work in the but maybe for n equal to do something in the one might be able to.
Abhay Vasant Ashtekar: see if, in fact, that is then realized we transform you know complex fire or whatever along the same lines that you're talking about just now that that would also be very nice to proceed.
Konstantin Eder: To mean for me, wants to.
Abhay Vasant Ashtekar: say it again.
Konstantin Eder: Because.
Konstantin Eder: gravity or.
Konstantin Eder: yeah.
Abhay Vasant Ashtekar: super super gravity so so generalize because I mean various people I mean particularly Tomas had that written down this complex if I send your lives we transform and the face space, so we can do the same thing.
Abhay Vasant Ashtekar: In put put in the quantity so super gravity, because in that case, then there is this this all these questions disappeared disappeared I they do disappear in the the Masonic sector, if you like it, because the group is compact, and therefore you can now have normalized had a major then.
Abhay Vasant Ashtekar: You can actually you can syndicate consistency and so on, and then, finally, you want to make.
Abhay Vasant Ashtekar: The final results you would like to make it like like once getting physical states you're like to make a loop public transport a generalized the transfer window states in order to get the ones in the audience that signature to something like that might be useful here as well.
Konstantin Eder: And context of transactions theories, with a supergroup because they observe this complex supergroup.
Konstantin Eder: They also am consider as how to.
Konstantin Eder: make sense of.
Konstantin Eder: compact groups in this context and they they call this a CES group because i'm generically supergroup sephora very simple structure, you have a persona crew and the algebra so this both quantities completely cold you're super group.
Konstantin Eder: And then he replaced this complex persona group in terms of the compact real form, and this is consistent, this case fortune Simon says in the call yeah so study consumers and Simon says PCs super groups to sing some comic relief form of the Masonic group.
Konstantin Eder: So they also deal with this kind of question this context.
Abhay Vasant Ashtekar: yeah so I mean the same similar question would come up exactly because if you're just able to find that graph then.
Abhay Vasant Ashtekar: You would just have a normal you would I would not compact group which you'd like to accomplish group and maybe you might be able to do the.
Abhay Vasant Ashtekar: Similar constructed as what they're doing here.
Jorge Pullin: Other questions.
Abhay Vasant Ashtekar: Okay, just one last piece so with this slide that we have got here.
Abhay Vasant Ashtekar: I mean, in the way that the entropy calculations done in Luke on gravity is quite different from the way it is then in.
Abhay Vasant Ashtekar: In string theory and therefore some relation between them would be very nice but it seemed to me that you are really focusing on the way it is done in string theory.
Abhay Vasant Ashtekar: And not really looking at sort of, say, the quantum geometry of the horizon, or would you be looking at the quantum geometry of the horizon and then relating it to the superpower filters or something which which which which, which is used in string theory.
Konstantin Eder: yeah probing just various aspects of the theory so getting a proper understanding of this consignment theories and boundaries of freedom was your theory so i'm.
Konstantin Eder: i'm.
Konstantin Eder: Standing a bit better.
Konstantin Eder: Because it's also related to the group presentations we are using here and it's actually similar questions we have an episodic theory.
Konstantin Eder: So yeah studying the presentations you want to consider if this is the continuous series interesting because three it serious and it's also addressed it's actually addressed here, in this context you have.
Abhay Vasant Ashtekar: Okay, thank you very much.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay let's Thank you again.