WEBVTT

1
00:00:03.500 --> 00:00:16.480
Hal Haggard: Hello and welcome. It's my pleasure to introduce Dongshu Q. Who will be speaking about spikes and spines in 3D. And 4 d. Lorentzian Simplicia quantum gravity. Dongshu.

2
00:00:16.730 --> 00:00:32.420
Dongxue Qu: Thank you. Thank you for the introduction, and thank you all for being here today. It's my pleasure to get to spend some time with you. This work is in collaboration with Johanna Bianca and Mark, based on these 2 papers.

3
00:00:33.040 --> 00:00:34.210
Dongxue Qu: So

4
00:00:34.240 --> 00:00:37.050
Dongxue Qu: first, st this is the plan of today's talk.

5
00:00:37.050 --> 00:00:38.979
Abhay Vasant Ashtekar: We? We don't see your slides.

6
00:00:39.600 --> 00:00:40.800
Dongxue Qu: Oh, really

7
00:00:42.810 --> 00:00:44.220
Dongxue Qu: sorry, can you?

8
00:00:44.220 --> 00:00:46.490
Hal Haggard: Didn't see them. Well.

9
00:00:46.990 --> 00:00:48.470
Hal Haggard: I can smell it, too.

10
00:00:48.960 --> 00:00:50.310
Hal Haggard: You can keep them up.

11
00:00:53.890 --> 00:00:56.090
Dongxue Qu: So you can see the slides right.

12
00:00:56.090 --> 00:00:56.960
Hal Haggard: Yes.

13
00:00:58.000 --> 00:00:58.460
Dongxue Qu: So.

14
00:00:58.460 --> 00:01:02.249
Hal Haggard: Like most people can see them. Let us know, Abby, if there's further issues.

15
00:01:03.370 --> 00:01:04.580
Hal Haggard: go ahead. Dongshu.

16
00:01:04.580 --> 00:01:30.790
Dongxue Qu: Okay, cool. So this is a plan of today's talk. First, st I will introduce the motivation of the study, and then I will go to some knowledge about the Lorenzan geometry or simplicity. 1st introduce what is complex reaction, and what kind of configurations we call them Letcom regular or letcom irregular configuration, and then introduce the triangle inequalities.

17
00:01:30.790 --> 00:01:43.089
Dongxue Qu: And what? How can we compute or get the asymptotic behavior or rejection? Then in the end we will go to the concrete examples in 3D. And 4 d.

18
00:01:44.940 --> 00:02:03.580
Dongxue Qu: Okay, so to understand the motivation of this study, we 1st need to recognize the main challenges that quantum gravity faces. One of the biggest issue is how to ensure the finiteness of the path integral and avoid singularities.

19
00:02:03.820 --> 00:02:25.929
Dongxue Qu: One of the main approach to help us with. This is using the simplation method, such as quantum logic calculus, and the spin forms which allows us to reduce the infinite dimensional path integral to the finite one by using the by discretizing the spacetime with the triangulations.

20
00:02:25.930 --> 00:02:37.820
Dongxue Qu: then the triangulations will act as regulators, and which help us to perform the pass integral into over the finite number of Edgelands.

21
00:02:38.070 --> 00:02:47.870
Dongxue Qu: However, even with the triangulations, we still face the risk of divergence. So the divergence, like a

22
00:02:48.030 --> 00:03:03.750
Dongxue Qu: when we talk about, or when we're dealing with the configurations, what we call the specs and the spans. These are situations where the bulk edges they can grow infinitely large, will maintain the boundary edge as small and fixed.

23
00:03:03.860 --> 00:03:24.249
Dongxue Qu: So when we're talking about this kind of configurations, especially in Euclidean quantum calculus, people already proved, they have infinite values for the partition function and the length expectation values. So it's a big deal in the Euclidean quantum calculus.

24
00:03:24.300 --> 00:03:38.839
Dongxue Qu: And on the other side, these configurations also make it a challenge to achieve the desired continued limit, where we hope the average edge length should be very small

25
00:03:39.990 --> 00:03:54.809
Dongxue Qu: for the specs configurations which is more challenging because it has a bulk vertex with some of the bulk edges, and we fix the boundary edge of we fix the boundary edge lens.

26
00:03:54.880 --> 00:04:10.429
Dongxue Qu: However, the interesting thing for the specs configuration is that we found out in the Lorentzian setting. Actually, in the end, we can get the finite value, partition function, and the finite length expectation values.

27
00:04:10.430 --> 00:04:26.239
Dongxue Qu: So it's a big deal, because it means in the Lorenzan setting. We can avoid the divergence in the Euclidean ones. So it means, okay, maybe the Lorenz setting can help us to fix this problem.

28
00:04:26.270 --> 00:04:30.519
Dongxue Qu: And, on the other hand, we also found out in the

29
00:04:30.620 --> 00:04:58.240
Dongxue Qu: Specs configuration, we have some light cone, irregular configurations which introduce some complex terms, or the imaginary terms to the complex rejection and the branch casts in the Lorentz integral control. So it means, if we want to defend the Lorentz integral properly, we 1st need to deal with these light cone irregular configurations.

30
00:04:58.300 --> 00:05:12.270
Dongxue Qu: and this is for the specs configuration for the spans configuration. So the boundary is still fixed, but the bulk edge will only have one bulkage, and this can stretch it to be infinity large

31
00:05:13.110 --> 00:05:38.040
Dongxue Qu: and for the specs, configurations. We also found out in the Lorentzian setting. It has a finite partition function values and the length expectation values, and it also has the light cone irregular configurations. The interesting thing is this kind of spans. Configurations can only appear in the Lorentzian triangulations because of the triangle inequality.

32
00:05:38.230 --> 00:05:56.469
Dongxue Qu: and till now there have no this. We there are no discussed in the simplation approaches, such as the spin forms, and we are going to talk about the specs and the spin spans configuration in our study.

33
00:05:57.450 --> 00:05:59.330
Dongxue Qu: So now you can see the.

34
00:05:59.330 --> 00:05:59.970
Florida Atlantic U: 2.

35
00:05:59.970 --> 00:06:00.670
Dongxue Qu: Yes.

36
00:06:00.960 --> 00:06:12.879
Florida Atlantic U: I wanted to ask you a question, though. So you mentioned this apparently well-known result that you have these divergences in Euclidean. Quantum merging calculus. I'm a little bit confused because there's this paper from

37
00:06:13.070 --> 00:06:16.180
Florida Atlantic U: 2,012 that Carlo wrote with

38
00:06:16.682 --> 00:06:29.050
Florida Atlantic U: Mario's Cristadulu and Aldo and others where they showed that at least, if you use them, I mean if the if the integrand is just the exponential of the

39
00:06:29.050 --> 00:06:50.189
Florida Atlantic U: Reg, a action without any sum over orientations that the spikes aren't divergent. That was the main result of that paper, but that was in 3D. Quantum gravity. So I was. I just wanted to understand how what you were saying about these divergences is consistent with that? Are you using cosine as the integrand in those results, or in these well-known divergences, or what.

40
00:06:50.190 --> 00:06:56.330
Dongxue Qu: So here for the intergrant, we just use E to the power of action.

41
00:06:56.430 --> 00:06:59.679
Dongxue Qu: ee. The action, and because

42
00:06:59.790 --> 00:07:07.700
Dongxue Qu: for the specs configuration we need to talk about how to send the back edge lens to infinity. So.

43
00:07:07.700 --> 00:07:10.250
Florida Atlantic U: Is there, so? Is there some over orientations.

44
00:07:11.182 --> 00:07:12.630
Dongxue Qu: Yes, we need to.

45
00:07:12.630 --> 00:07:13.440
Florida Atlantic U: Okay.

46
00:07:13.440 --> 00:07:14.210
Dongxue Qu: Patience.

47
00:07:14.810 --> 00:07:23.979
Florida Atlantic U: Okay, good. So that's the difference. So I guess the point was with this 2,012 paper. The point was, if you don't sum over orientations. Then you also get finiteness in the Euclidean case.

48
00:07:24.780 --> 00:07:35.819
Dongxue Qu: Yes, but I'm not sure that paper, but at least in this 2D. Euclidean, Reggie. They very well proved that the partition function is infinite.

49
00:07:36.360 --> 00:07:40.069
Dongxue Qu: So, but I will check the 3D papers to see.

50
00:07:40.070 --> 00:07:40.520
Florida Atlantic U: Okay.

51
00:07:40.520 --> 00:07:41.039
Dongxue Qu: The result.

52
00:07:41.040 --> 00:07:41.680
Florida Atlantic U: Thank you.

53
00:07:41.680 --> 00:07:42.280
Dongxue Qu: Okay?

54
00:07:43.040 --> 00:07:58.250
Dongxue Qu: Alright. So that's basically the idea of why we want to look at the specs and the spans configurations. And you can figure out both specs and the spans. They are crucial in the 3 and the 4 d. Lawrence and settings.

55
00:07:58.270 --> 00:08:17.760
Dongxue Qu: and our research will focus on how specs and spans behave across different dimensions, and we aim to address the issues of divergence by investigating whether the specs and the spans configuration lead to finite or divergent path integral.

56
00:08:17.760 --> 00:08:32.899
Dongxue Qu: and how we can ensure the finite results in the Lorentz integral, and at the end of the day we hope we can improve the understanding of the quantum gravity by exploring how specs and spans

57
00:08:32.900 --> 00:08:38.879
Dongxue Qu: influence the overall structure and the behavior of Lauran Pass. Integral.

58
00:08:39.020 --> 00:08:49.910
Dongxue Qu: Okay, so this is a motivation. And before we go to the concrete examples, let me introduce some background knowledge about Lorentz and geometry or simplicity.

59
00:08:50.570 --> 00:09:08.699
Dongxue Qu: So let's start with the complex rejection. And that's how we approach quantum gravity through the simulation method. So just as a quick reminder, this is the Reggie Pass integral, and we are thumbing over all the possible geometries.

60
00:09:08.700 --> 00:09:32.989
Dongxue Qu: In our case we are summing over all the possible bulk edge. So this is the bulk edge and the S represent the complex rejection. So that's where things get interesting. You can see the complex rejection include both the bulk hinge and the boundary hinge. So hinge is d minus 2 dimensional simplex.

61
00:09:32.990 --> 00:09:55.540
Dongxue Qu: And here, Vh, is the squared volume. We can compute it by using what we call the clean measure determinant. As long as we are given the edge length, we can always compute the squared volume and the signature of the squared volume actually already tells us which type of the Simplex.

62
00:09:55.540 --> 00:10:03.399
Dongxue Qu: if the squared volume, greater than 0, then it is a space lag. If it's less than 0, then the Simplex is time lag.

63
00:10:03.680 --> 00:10:07.199
Dongxue Qu: and the the magic happens at this

64
00:10:07.320 --> 00:10:34.909
Dongxue Qu: dihedral angle so we can get the deficit angle. The deficit angle tells us the curvature at each hinge, and we can compute the deficit angles by using the definition of the complex dihedral angles and the complex dihedral angles can compute it by using this formula. Here the branch cut of the logarithm and the

65
00:10:35.050 --> 00:10:38.139
Dongxue Qu: square root we adapt to this convention

66
00:10:38.711 --> 00:10:43.200
Dongxue Qu: the beauty of this complex diarangle is that

67
00:10:43.260 --> 00:11:05.530
Dongxue Qu: we use one formula to capture both Euclidean and Lorentz angle. So, for example, if we are given a time-like triangle, then we end up with a Euclidean angle. If we are given a space-like triangle, then we will deal with the Lorentz angle.

68
00:11:05.590 --> 00:11:30.919
Dongxue Qu: So in the case of the Euclidean angle, you can see actually, the complex dihedral angle can reproduce this Euclidean angle, and then we get the regular Euclidean deficit angles, which means here the complex rejection will be purely imaginary, resulting in the integrand. Here will be real.

69
00:11:31.650 --> 00:11:52.570
Dongxue Qu: And let's switch over to the Minkowski angle, which everything is getting a little bit complicated. So this is the Lorentz and dihedral angle which is complex, the real part of the Lorentz and dihhedral angle. You can see this is the actual physical

70
00:11:53.062 --> 00:12:02.409
Dongxue Qu: angle. But for this imaginary part we have this M value. So the meaning of this will depends on

71
00:12:02.410 --> 00:12:23.809
Dongxue Qu: how many light reads included between the edge of the edge, between A and B. So, for example, if A and B, they sit in one quadrant. It means there is no light ray between A and B, then this m is equal to 0. But if A and B, they sit in different quadrants.

72
00:12:23.880 --> 00:12:30.550
Dongxue Qu: and there are one or 2 letters. Then this M value will be equal to one and 2.

73
00:12:30.740 --> 00:12:45.599
Dongxue Qu: Okay, so then they have. They can also reduce this complex daherent angle to the regular, to the Lorentz and daherent angles. And this is the Lorentz and deficit angles. So you can see if

74
00:12:45.640 --> 00:12:56.400
Dongxue Qu: this sum OM. Equal to 4, which means the sum of the dihedral angles at the hinge will include 4 letters.

75
00:12:56.430 --> 00:13:06.640
Dongxue Qu: that is, 2 light cones. In this case we have the light cone, regular configuration, and the action at this hinge will be real.

76
00:13:06.790 --> 00:13:17.989
Dongxue Qu: Okay? So then, it means, if we have the light cone, regular configuration, which include 4 light cones, we will have the real rejection. But

77
00:13:18.980 --> 00:13:21.430
Dongxue Qu: if I saw a question.

78
00:13:23.498 --> 00:13:35.229
UP: Whitmore 320: Ask a technical question about the sign of Beta or this angle. Is it real? Is it positive? What is there a convention.

79
00:13:36.438 --> 00:13:37.630
Dongxue Qu: You mean this one.

80
00:13:37.630 --> 00:13:38.490
UP: Whitmore 320: Exactly.

81
00:13:38.640 --> 00:13:39.220
Dongxue Qu: Okay.

82
00:13:40.310 --> 00:13:45.509
Dongxue Qu: yes, this is the. It will be real, and it's the physical angle.

83
00:13:46.020 --> 00:14:02.950
Dongxue Qu: So we can compute it by cosine cosine or hypersine and hyper cosine, and I think Sorkin has the Raphael Sorkin. They have a very detailed paper on how to compute this Beta values.

84
00:14:03.440 --> 00:14:16.719
UP: Whitmore 320: Good. Thank you. I was wondering if the sign depends on if, like 2 time, like vectors, are both future pointing or one fussial pointing and one plus pointing that is encoded into the sine of Beta.

85
00:14:17.650 --> 00:14:19.060
Dongxue Qu: Hmm

86
00:14:23.595 --> 00:14:31.859
Dongxue Qu: this, I'm not sure. But I think in the end the site. If, for example, if it's 1

87
00:14:31.880 --> 00:14:33.640
Dongxue Qu: pointed to the

88
00:14:33.710 --> 00:14:37.280
Dongxue Qu: past, 1 point to the future.

89
00:14:37.390 --> 00:14:43.059
Dongxue Qu: the for the hyper sign. It will have the signature difference.

90
00:14:44.810 --> 00:14:45.840
UP: Whitmore 320: Okay. Thank you.

91
00:14:46.150 --> 00:14:46.920
Dongxue Qu: You're at.

92
00:14:48.160 --> 00:15:09.809
Dongxue Qu: Okay. So this is the light cone, regular configuration. And for the light cone irregular configuration, it means, okay. So now the sum of the M. Value is not equal to 4, it can be more or less than 4. Then in this case you can see the Lorentzian deficit angle will be complex.

93
00:15:09.820 --> 00:15:37.260
Dongxue Qu: and here we have the light cone. Irregular configuration. It means at the sum of the dihedral angles at the hinge will have more or less than 2 light cones, and in this case we will introduce a positive or negative imaginary part to the radio action. And here you can see. Actually, there is a branch cut in the action along the light cone. Irregular configurations.

94
00:15:37.340 --> 00:15:39.560
Dongxue Qu: Okay, so then.

95
00:15:39.990 --> 00:16:04.930
Dongxue Qu: actually, this light cone, irregular configurations appear typically, when the topological change happens, and this topological change plays an important role by the derivation of entropy from the Lorentz integral. And then we characterize this light cone. Irregularity characterize the point on the manifold

96
00:16:04.930 --> 00:16:18.620
Dongxue Qu: with more or less than 2 light cones. So, for example, this trouser configurations, this one has 4 light cones, and for this Yarmok configuration. This one has 0 light cones.

97
00:16:20.780 --> 00:16:43.539
Dongxue Qu: And then actually, in the previous study, how we found out the light cone irregularity. Actually, they have been observed in the cosmological evolution with the small bulk edge regime. And in our study we found out actually, this kind of light cone irregularity can also happen in the large bulk edge

98
00:16:45.576 --> 00:17:00.490
Dongxue Qu: here. We want to see. Actually, you can see there is an imaginary term in the complex rejection, and it can be positive it can be negative. Actually, the sound of this imaginary term

99
00:17:00.560 --> 00:17:22.399
Dongxue Qu: cannot be fixed. It will depend on the convention we adopt, especially when we complexify the bulk edge lens. So we have 2 different kind of complication for the bulk, for the squared edge lens. Then in the end we will have either positive or negative, then.

100
00:17:22.589 --> 00:17:32.919
Dongxue Qu: in the short term, it means the sound of the imaginary terms in the ready action will depend on which set we choose to approach the branch cut.

101
00:17:33.170 --> 00:17:56.020
Dongxue Qu: and in this sense it means, if we want to deal with the light cone irregularities in the path integral. First, st we need to decide whether we want to include this light cone. Irregularity. If we do want to include it, then which side we need to choose when the branch casts are infinity long.

102
00:17:56.020 --> 00:18:10.000
Dongxue Qu: So here we need to choose the set that surprise, the contribution from the light cone, irregular configurations. So that's we can make the we can make the pass integral stable.

103
00:18:10.200 --> 00:18:28.170
Dongxue Qu: Okay, so this is like irregularity. And for the triangle inequality, this will help us decide a given simplex whether we can embed it into the flat Euclidean or Laurentian space.

104
00:18:28.170 --> 00:18:51.969
Dongxue Qu: So for the Euclidean one, it's pretty easy if we are given a space like Simplex Sigma. Then the Simplex itself and the subsymplicity. All of them should be space like, for example, if this triangle, it's space like, then the squared area and the square edge length. All of them should be greater than 0.

105
00:18:52.310 --> 00:19:15.649
Dongxue Qu: But for the Lorentz ones it will be a little bit complicated, because for the Lorentz Simplex it will include both the time, like space, time, like space like, and the null simplex. And if Rho is a time like Simplex or not, then the all the sub simplex

106
00:19:15.650 --> 00:19:36.190
Dongxue Qu: containing this row should be time-like or not. For example, here for this Tyturan. If we are given this edge 0 1, it's time-like. Then the Tatian itself and the adjacent area 0 1, 2, and 0 1, 3. They should be time-like.

107
00:19:36.520 --> 00:19:53.170
Dongxue Qu: but for the triangle 0 2, 3, and the 1, 2, 3, they can be spaced like a 10, like or no. So by using this triangle inequality, we can also determine whether we can scale one edge to infinity large.

108
00:19:53.400 --> 00:20:23.090
Dongxue Qu: So this is impossible in the Euclidean case, because in Euclidean case we can't fix. For example, if we are talking about a triangle, we can't just fix 2 edge and makes one of them infinitely large. But this can happen in the Lorentzian setting. So, for example, if we have a triangle, and one of them are space, like 2 of them are time like or the opposite. 2 of them are time, like 2 of them are space like one of them, are

109
00:20:23.090 --> 00:20:34.329
Dongxue Qu: spacelike. Then this Lorentzian triangle inequality will be always satisfied, which means we can stretch this as 0 1 to be infinity large.

110
00:20:34.670 --> 00:20:36.910
Dongxue Qu: And actually this

111
00:20:37.240 --> 00:20:50.560
Dongxue Qu: triangle inequality will also help us whether a given simplex is all the triangulation is allowed or forbidden. So, for example, in the Epr spin form.

112
00:20:50.560 --> 00:21:08.950
Dongxue Qu: We have the 4, 1 more, and for this 4, 1 more. We can't have the triangulation with the space like we have the boundary space like a tetrahedron and make the space like bulkhead infinitely large. This is forbidden in the Epr spin form.

113
00:21:10.280 --> 00:21:30.099
Dongxue Qu: Okay? So then, how to derive the asymptotic behavior of the rejection. So this is the rejection. And in order to have the asymptotic behavior of the reg action, we need to have the asymptotic behavior of the volume or the squared volume first, st and then

114
00:21:30.100 --> 00:21:41.699
Dongxue Qu: by deriving it in the limit of the single large edge or the multiple out large edge. We can see, for example, for this Tetrian

115
00:21:42.195 --> 00:21:58.850
Dongxue Qu: the square, the volume of the Titerium, the leading order terms coefficient actually depends on the area. It's kind of the dimensional reduction, and by using this kind of dimensional deduction reduction, actually, all this

116
00:21:58.950 --> 00:22:05.639
Dongxue Qu: dihedral angles bulk edge the deficit angles and the deficit angle set to the boundary bulk.

117
00:22:05.700 --> 00:22:11.260
Dongxue Qu: All of them will be very simple results in the asymptotal regime.

118
00:22:11.340 --> 00:22:29.910
Dongxue Qu: and because of the dimensional reduction, actually, the asymptotic behavior or reject action is also simple. For example, 3. To move. You can see the regime's leading order. Coefficient is just a 2 pi.

119
00:22:30.100 --> 00:22:53.329
Dongxue Qu: and especially in 2D. Reg action. We know it's invariant, and we don't see any. We don't see the boundary data dependence on the for the leading coefficient. So this is because of the dimensional reduction, and we will adapt the whole idea for the for the whole study for the 3D. And the 4 d.

120
00:22:54.050 --> 00:22:58.150
Dongxue Qu: Okay, so now we can go to the concrete example

121
00:22:58.310 --> 00:23:16.390
Dongxue Qu: for the 3D. The span, the span configuration. We will use the 3, 2 pact mode and the 3 2 pact model. Actually, it has the initial configuration. The initial configuration has 3 touch. Here they share one bulk edge.

122
00:23:16.470 --> 00:23:28.910
Dongxue Qu: and if we integrate out this back edge we will have the final configuration, which only has 2 tetrahedron, and here we only focus on the initial configurations.

123
00:23:29.070 --> 00:23:39.849
Dongxue Qu: and then we will fix the boundary geometry and push this bulk edge to be infinity, it can be positive. Infinity can be negative infinity.

124
00:23:39.880 --> 00:23:49.049
Dongxue Qu: And the asymptotic behavior, as we discussed before, we have the asymptotic behavior. The leading coefficient is just 2 pi.

125
00:23:49.480 --> 00:23:57.190
Dongxue Qu: So let's look at the 1st example. If we fix the boundary geometry as spacelike, and they remain constant.

126
00:23:57.210 --> 00:24:00.540
Dongxue Qu: and the the bulk hedge is time. Lag.

127
00:24:00.640 --> 00:24:12.250
Dongxue Qu: So you can see this solid land. It's the it's the actual result or the numerical result of the 3 2 Regi action

128
00:24:12.370 --> 00:24:15.720
Dongxue Qu: in the large bulk regime

129
00:24:15.910 --> 00:24:21.939
Dongxue Qu: you can see it approached the asymptotic result very much, and

130
00:24:22.130 --> 00:24:36.040
Dongxue Qu: the leading order. It's also real, which means we have the light congregular configuration, although here, you can see, we have a imaginary part. But this imaginary part is constant.

131
00:24:36.040 --> 00:24:52.930
Dongxue Qu: This is because we have the convention for the density angle. And actually we can change the convention and make this imaginary part the constant imaginary part vanish. So here, if you want to decide, the

132
00:24:53.030 --> 00:25:08.440
Dongxue Qu: configuration is regular or irregular. We will look at the imaginary part to see whether it change with the bulk edge. So, anyways, this is the example. The configuration is like con regular.

133
00:25:08.540 --> 00:25:32.190
Dongxue Qu: Then let's look at the next example. We still fix the boundary edge as space like, but the bulk edge are also space like. So here the bulk edge should be greater than 3. This is because of the triangle inequality. Then they push it to infinity large. You can see the leading order term is purely imaginary.

134
00:25:32.220 --> 00:25:39.310
Dongxue Qu: So this means we have the light cone irregularly irregular configuration, and

135
00:25:39.350 --> 00:25:54.550
Dongxue Qu: in this case, once the light con irregular configuration appears, we need to decide which part of which integration control we need to choose, then we can make the integration converge.

136
00:25:54.690 --> 00:26:00.680
Dongxue Qu: Okay, so this is the example. We have the Letcom irregular configuration.

137
00:26:01.190 --> 00:26:26.200
Dongxue Qu: Actually, the previous 2 examples restrict this 3 touch here and they are same. Actually, we can relax this condition and make these 3 touch here are different. In this case you will see the light cone, regular configuration and the light cone. Irregular configuration will happen in the same triangulations.

138
00:26:26.200 --> 00:26:33.719
Dongxue Qu: So this is the region. We have the light con regular regime, and then we also have the

139
00:26:33.890 --> 00:26:37.590
Dongxue Qu: regime, which is a lightcome, irregular configuration.

140
00:26:39.020 --> 00:26:58.980
Dongxue Qu: So actually, we can generalize this discussing for the 3, 2 more to any configurations which has untouched. They share one bulk edge. And this is the asymptotic behavior. You can see the leading order actually is independent of the N values.

141
00:26:59.160 --> 00:27:00.820
Dongxue Qu: And actually.

142
00:27:01.030 --> 00:27:09.450
Dongxue Qu: for this asymptotic behavior, it has the implication for the Lawrence and personnel Regi model. Here, in.

143
00:27:09.530 --> 00:27:22.659
Dongxue Qu: Actually, one can define a 5th space in the ready calculus, and we have the length variables. These length variables will be conjugated to the boundary deficit angles.

144
00:27:22.770 --> 00:27:29.059
Dongxue Qu: and in this space, in this face space for time, like edge.

145
00:27:29.110 --> 00:27:38.980
Dongxue Qu: the boundary, we will see. The boundary depth angle will be compact, and the one will expect. The lens operator has a discrete spectrum.

146
00:27:39.200 --> 00:27:44.699
Dongxue Qu: but the force speaks like edge. The boundary deficit angle is non-compact.

147
00:27:44.780 --> 00:27:49.790
Dongxue Qu: and one will expect the lens operator has a continuous spectrum.

148
00:27:49.870 --> 00:28:03.209
Dongxue Qu: Actually, these expectations are indeed satisfied in the Lorenz and Pasano Reggie model, because for the spectrum of the time like lens, it will goes like this.

149
00:28:03.600 --> 00:28:27.470
Dongxue Qu: and it is approximate by J. In large regime G will be the integers, and here the amplitude will be well expressed by one. If we ignore the major terms and the boundary terms. So this means what we get here has some implication for the Lorentz and Panzano ready model.

150
00:28:31.610 --> 00:28:34.039
Dongxue Qu: So okay, let's go to the

151
00:28:34.140 --> 00:28:44.359
Dongxue Qu: next example in 3D. Which is the spec configuration and the full spec configuration, we will use the 4 1 packed mode. So the

152
00:28:44.400 --> 00:29:05.160
Dongxue Qu: initial configuration for the 4 1 packed move. We have 4 tetrah here and there is one bulk vertex. So this bulk, vertex, we can stretch it. Then it means this 4 bulk edge can grow up to large, where we maintain the boundary geometry fixed.

153
00:29:05.740 --> 00:29:16.830
Dongxue Qu: So here, because we have 4 bulk variables, but in this case the rejection is a constant. It means we have 3 dimensional gauge orbits.

154
00:29:16.860 --> 00:29:31.170
Dongxue Qu: Then we need to do the gauge fixing here we choose the gauge fixing is this tab we call the detailed scaling. It means all the back edge. In the large regime we choose they are equal.

155
00:29:31.260 --> 00:29:49.349
Dongxue Qu: and in this case we have. We also do the same thing to compute the asymptotic behavior of the radiation, and for different cases, the homogeneous case and the inhomogeneous case. We have different kind of the asymptotic behaviors.

156
00:29:49.360 --> 00:30:06.090
Dongxue Qu: and for the time, like bulk edge, you will see it will be always light, con, regular, and for the asymptotic regime. If it includes the space like bulk edge, we will have the light con irregular configurations.

157
00:30:06.300 --> 00:30:07.700
Dongxue Qu: and that

158
00:30:08.060 --> 00:30:09.040
Dongxue Qu: so

159
00:30:09.500 --> 00:30:18.309
Dongxue Qu: we can make some discussion before we go to the finite expectation values. You will see for the time, like bulk edges.

160
00:30:18.320 --> 00:30:39.769
Dongxue Qu: the rejection will be real which gives us the light congregular configuration. If if it's light congregular configuration, which means the exponential, the integrand of the exponential will be surprised, and this lead us to a convergence of the pass integral.

161
00:30:39.770 --> 00:31:04.480
Dongxue Qu: But if we have the space like bulk edge, then it will give us the light cone irregular configuration in the rejection, and here we will have an imaginary term which gives us a sand which can be positive can be negative, and this is because we have the branch cuts along the Laurentian configuration.

162
00:31:04.610 --> 00:31:26.289
Dongxue Qu: And here we need to decide which side we need to integrate out along the branch cuts. So here we can't choose the imaginary part of the action less than 0, because this will cause the divergence. So we need to choose. The imaginary part of the action will be greater than 0 to make it a stable.

163
00:31:27.310 --> 00:31:50.780
Dongxue Qu: And so that's for the potential function. And actually, we can compute the finite expectation values for the arbitrary power or lens and for the expectation values. Actually here we use the numerical method called the vince epsilon algorithm. Then we can compute the exact expectation values.

164
00:31:50.780 --> 00:32:17.489
Dongxue Qu: And for the because we want to compare it with the asymptotic behavior. So we can also compute the asymptotic behavior of the rejection. And here we use the 3, 2 more as an example, and we can also get the asymptotic behavior of the measure. In the end we got the asymptotic approximation of the expectation values in this form.

165
00:32:17.530 --> 00:32:32.560
Dongxue Qu: And here we have a E function. This E function will be always finite. So it means this asymptotic value for this integration, for this expectation value will be always finite.

166
00:32:33.510 --> 00:32:56.410
Dongxue Qu: And here, actually, we have the finite result. It's not surprising, because actually, the accelerated nature of the Lorentz interval gives us this finite result, although the intergrant is oscillate highly, but in the end they will cancel each other. In the end we get the finite result.

167
00:32:57.220 --> 00:33:06.989
Dongxue Qu: and we compare the asymptotic result with the with the exact result. And here you can see they matched very well.

168
00:33:07.050 --> 00:33:11.009
Dongxue Qu: So this is the finite expectation values.

169
00:33:11.520 --> 00:33:40.070
Dongxue Qu: And for the 3D case we discussed many different cases with light cone, regular and light cone, regular irregularity, and for the light cone irregular configuration. Here we introduce a complex behavior in the pass integral, and you can see the asymptotic behavior or the action, which is very simple, especially for the leading order. The coefficient is either 2 pi or 4 pi.

170
00:33:40.430 --> 00:34:01.659
Dongxue Qu: And we here we also found a very simple method which can identify whether allowed asymptotal regime based on the triangle inequality, and this allows us to determine whether we can embed a triangulation into a flight Euclidean or Lorentzian space.

171
00:34:01.730 --> 00:34:14.090
Dongxue Qu: and we also found some certain configurations that the large space, like the large space, like bulk edge, are forbidden by the Laurent triangle in cautious.

172
00:34:14.730 --> 00:34:33.519
Dongxue Qu: So about the financialness of passing to grow. First, st we need to decide whether we want to include this in irregular configurations. If we want to include them, then we need to choose the surprising side of the branch cut for the integration control.

173
00:34:33.530 --> 00:34:44.309
Dongxue Qu: and the next, this fanatinous result also hold for both the asymptotic regime and asymptotic method and the numerical method.

174
00:34:44.330 --> 00:34:53.420
Dongxue Qu: And we expect this also the true nature of the Laurentian pass. Integral ensures the finite results.

175
00:34:54.239 --> 00:35:17.099
Dongxue Qu: Okay, so this is the 3D cases, and for 4 D cases we will adapt the similar algorithm first, st for the span configuration. In 4 d. We use the 4, 2 packed move and for 4 d. Packed move the initial configuration. We have 4 4 simplicities. They share one bulk edge.

176
00:35:17.260 --> 00:35:18.620
Dongxue Qu: and the

177
00:35:18.720 --> 00:35:31.010
Dongxue Qu: here we will have the bulk triangles. This bulk triangles type will depend on the the bulk edge. We choose it time like, or space like.

178
00:35:31.090 --> 00:35:36.080
Dongxue Qu: And here we also need to consider the low random triangle inequality.

179
00:35:36.290 --> 00:36:02.510
Dongxue Qu: So the 1st example here we choose the boundary edge length. They are space like and remain constant, and the shared bulk edge. We choose it time like, and push it to infinity. In this case you can see the leading order is still real, so it means in the asymptotal regime. We only have the Lat congregular configuration or the Latin regular bulk triangles.

180
00:36:02.510 --> 00:36:11.229
Dongxue Qu: and here the all the triangles should be the bulk triangles. They will be time like, because the bulk actually is time, like

181
00:36:12.420 --> 00:36:33.569
Dongxue Qu: the next example is. If the bulk edge is space like, then in this case, if we only look at the large edge regime, you can see it's still the light cone regular. There is no light cone regular configuration in the large J regime. But

182
00:36:33.830 --> 00:37:03.470
Dongxue Qu: if we look at the small edge regime, you will see. Okay, actually the imaginary part of the action. It is changing. So it has some light cone irregular configuration, but for the small edge regime. So here the conclusion is because we are looking at the asymptotic regime. Then in the asymptotal regime there is only the light cone, regular configuration.

183
00:37:04.910 --> 00:37:15.980
Dongxue Qu: and we can also generalize the consideration for 4 to move to unseen places which share one package. Then we have this

184
00:37:15.980 --> 00:37:37.429
Dongxue Qu: very simple asymptotic behavior for the radiation. And this asymptotic behavior actually also has some implication for the spin forms, because we know in the semi-classical regime the full simplex amplitude will approximate the cosine of the radiation.

185
00:37:37.530 --> 00:37:44.159
Dongxue Qu: and we also know for the time, like triangles in the spin form, it has the discrete.

186
00:37:44.260 --> 00:37:50.690
Dongxue Qu: the spectrum, and the area, how the absolute value in the half integers.

187
00:37:50.770 --> 00:38:07.620
Dongxue Qu: And here, if we have the, because we have the asymptotic approximation of the absolute value for the error, it follows this relation, then the expression for the action will reduce to this form.

188
00:38:07.620 --> 00:38:27.960
Dongxue Qu: and for the 4 2 move we know this 2 t. Minus n is equal to 4, then it means the amplitude can be well approximate by one. Here we also ignore the measure terms, because for the measure terms, if the areas are large, then it will suppress the amplitude.

189
00:38:28.220 --> 00:38:32.310
Dongxue Qu: Okay, so this is the implication for the spin forms.

190
00:38:33.070 --> 00:38:53.990
Dongxue Qu: and in the end we will talk about the spec configuration in 4 d. So in 4 d. We will use the file, one packed mode. So for the file file, one packed mode, the initial configuration we have file for simplicity. This file for simplicity have one bulk vertex.

191
00:38:54.000 --> 00:39:05.250
Dongxue Qu: and this bulk vertex gives us, because this, then we will have 5 bulk edges, and these file bulk edges will be integrated out

192
00:39:05.380 --> 00:39:09.409
Dongxue Qu: in the end. It will give us 10 bulk triangles

193
00:39:09.790 --> 00:39:34.039
Dongxue Qu: here, because we have file bulk variables with one constant rejection condition. It means here we will have 4 dimensional gauge orbits. Then we need to do the gauge fixing. We still adapt the addictive scaling method, which means in the larger edge regime. We will make this file bulk edge a same.

194
00:39:35.700 --> 00:39:52.590
Dongxue Qu: and we will. We discussed many different cases for the homogeneous case, and in homogeneous case, with different types of the bulk edge, and we found out the boundary we found out actually, this

195
00:39:52.850 --> 00:40:08.040
Dongxue Qu: asymptotic behavior or the radiation in the 4 dimensions will rely on the boundary data, especially for these 2 cases, the homogeneous case. If the bulkheads are time-like.

196
00:40:08.120 --> 00:40:18.260
Dongxue Qu: all them are time like you can see it's a light con regular, but the leading order will depends on the 3D Euclidean rejection.

197
00:40:18.310 --> 00:40:42.419
Dongxue Qu: So, but for the space like bulk edge, you can see the file. One more rejection will depend the leading order. Coefficient will depends on the Lorentzen 3D rejection. Then the type of the irregular configuration will depends on the boundary triangulations.

198
00:40:42.590 --> 00:40:44.296
Dongxue Qu: Okay? So

199
00:40:45.310 --> 00:40:50.850
Dongxue Qu: basically, we have, we will use this for 2

200
00:40:50.880 --> 00:41:19.970
Dongxue Qu: as an example to compute the finite expectation values in 4 d. And here, because we already have the rejection for the 4, 2 mu, and the leading order is pi lambda. We can compute the analytical approximation or the expected expectation values, and we can also compute the exact numerical values by using the wing algorithm.

201
00:41:20.090 --> 00:41:28.520
Dongxue Qu: And you can see the analytical result and the exact numerical result they matched very well.

202
00:41:30.370 --> 00:41:45.950
Dongxue Qu: so we can have the discussion for 4 d. Cases here. First, st we got a very simple asymptotic form for the Reggie action, and you can see the leading order. Term is typically order lambda.

203
00:41:45.950 --> 00:42:00.520
Dongxue Qu: But for the leading order term, next to leading order, terms will be to the order of square root lambda, which will depend on the boundary data. But for the order of Lambda it's independent of the boundary data.

204
00:42:00.620 --> 00:42:22.729
Dongxue Qu: and here we also have the light cone irregular configurations, so the bulk triangles. They may have some light cone. Irregular configurations, especially for those configuration has mixed signature cases with both the space like bulk edge and the time like bulk edge.

205
00:42:22.850 --> 00:42:27.710
Dongxue Qu: and the most of the let coin irregular bulk deficit angles.

206
00:42:27.810 --> 00:42:31.289
Dongxue Qu: Actually they are the Yarmok type.

207
00:42:31.460 --> 00:42:57.399
Dongxue Qu: because the coefficient is 2 pi. But actually we also may. We may also how the trouser type appears. It depends, because for the previous slides you will see the boundary. The rejection view depends on the boundary, the 3D. Boundary, Lorentz, and reject action. Then, in this case the trouser type may appear in the file, one move.

208
00:42:58.730 --> 00:43:06.225
Dongxue Qu: and especially for the generalized triangle. Inequality, it will help us determine.

209
00:43:06.940 --> 00:43:23.530
Dongxue Qu: the triangulations are allowed or forbidden. For example, in the spin forms the file. One more configuration with the spacelike boundary texture and the large space like bulk edge. This type of triangulation will be forbidden.

210
00:43:25.160 --> 00:43:41.159
Dongxue Qu: and for 4, 1 and 4, 1 and 4, 2 moves. It can be interpreted as the coarse grinding move, because this will helps us to understand the renormalization in the Lorentz and ready calculus and the spin forms.

211
00:43:41.590 --> 00:43:55.980
Dongxue Qu: and for the finite path integrals, because we have the Lorentz and Reggie calculation, or the Lorentz and Reggie Pass integral for the 4 1 and the 4, 2, 5, 1 and the 4, 2 move. They are finite.

212
00:43:55.980 --> 00:44:13.010
Dongxue Qu: and even for the arbitrary power of the length, expectation, values. We also have the finite result here. When we are going to deal with the oscillatory integration, we will use the numerical method called the bin algorithm.

213
00:44:13.070 --> 00:44:20.710
Dongxue Qu: So and here we expect this oscillatory property will give us this finite results.

214
00:44:21.790 --> 00:44:24.630
Dongxue Qu: Okay, so that's all. Thank you.

215
00:44:32.170 --> 00:44:33.739
Hal Haggard: Are there questions?

216
00:44:37.849 --> 00:44:42.040
Florida Atlantic U: I have a question. It's kind of a follow up question to my 1st

217
00:44:42.090 --> 00:44:53.580
Florida Atlantic U: question. So in the answer to my 1st question, you said that you were summing over orientations, but I don't think I saw that in your presentation, so so are you actually summing over orientations in this work, or.

218
00:44:53.580 --> 00:44:54.239
Dongxue Qu: In this world.

219
00:44:54.240 --> 00:44:55.300
Florida Atlantic U: Why not?

220
00:44:55.300 --> 00:44:55.759
Dongxue Qu: So you know.

221
00:44:55.760 --> 00:44:56.450
Florida Atlantic U: We don't.

222
00:44:56.450 --> 00:45:11.679
Dongxue Qu: Didn't. Yes, because we are talking about the Lawrence in case, and we only care about the regular case and do some numerical calculations for the regular configuration. We didn't consider the orientations.

223
00:45:12.460 --> 00:45:18.160
Florida Atlantic U: Okay? So if so the the divergences in the Euclidean case, so that they are happening

224
00:45:18.360 --> 00:45:21.759
Florida Atlantic U: without without even summing over orientations, you still get

225
00:45:21.940 --> 00:45:23.849
Florida Atlantic U: divergences. Is that what you're saying?

226
00:45:24.860 --> 00:45:37.779
Dongxue Qu: In the 2 dks so so we only so in the 1st slides we only see the 2 Dks for the 3 Dks. I didn't look into it.

227
00:45:38.090 --> 00:45:42.730
Dongxue Qu: I'm not sure what's the result in the 3D case. But I think

228
00:45:43.110 --> 00:45:45.650
Dongxue Qu: Bianca mentioned it before.

229
00:45:45.670 --> 00:45:51.380
Dongxue Qu: or even in 3D. Case it also has some divergence problem in Euclidean

230
00:45:51.520 --> 00:45:52.800
Dongxue Qu: Pass. Integral.

231
00:45:53.650 --> 00:45:58.969
Florida Atlantic U: Yeah. The question is whether it's with, with or without the sum over orientations you get the divergence.

232
00:45:59.681 --> 00:46:04.018
Florida Atlantic U: Another thing is with the when you. It's very nice, this

233
00:46:04.510 --> 00:46:12.980
Florida Atlantic U: this way, that you can get both the you both the Euclidean and the Lorentzian Reg action from the same action.

234
00:46:13.413 --> 00:46:22.080
Florida Atlantic U: And then you can naturally get the E to the minus Euclidean action in the Euclidean case and E to the I

235
00:46:22.350 --> 00:46:26.809
Florida Atlantic U: Lorentzian action in the Lorentzian case. Is that right? So.

236
00:46:30.120 --> 00:46:41.929
Florida Atlantic U: okay, so that would be another difference between what was done in this earlier work for 3D. Euclidean reg calculus is that the integrand used was E to the I

237
00:46:42.470 --> 00:46:49.329
Florida Atlantic U: action Euclidean, whereas here, with this nice unified framework in the Euclidean case, you get E to the minus

238
00:46:49.890 --> 00:46:52.339
Florida Atlantic U: Euclidean actions. And maybe that's a difference.

239
00:46:52.570 --> 00:47:02.780
Dongxue Qu: Yes, for the Euclidean case, then the action will be purely imaginary. So here, then, it's E to the minus the real action.

240
00:47:03.440 --> 00:47:04.060
Florida Atlantic U: Yes.

241
00:47:04.060 --> 00:47:04.404
Dongxue Qu: Hmm.

242
00:47:05.240 --> 00:47:18.559
Florida Atlantic U: So I'm wondering how much the finiteness results is due to the fact that you have E to the minus action you have E to the I action instead of E to the minus action. I'm not sure how much the finiteness has to do with that.

243
00:47:20.348 --> 00:47:36.739
Dongxue Qu: So for you can see the examples we are given so we are talking about the Letcom regular configurations, and for the light con regular configurations, the action will be fairly imaginary.

244
00:47:37.130 --> 00:47:47.789
Dongxue Qu: So which means the it's E to the negative real action. Then all of them we got the finite results. I do think it depends on

245
00:47:47.890 --> 00:48:17.080
Dongxue Qu: like whether the action is imaginary or poorly imaginary or not, but for the like irregular configurations. Here we will choose, because we have the imaginary part for the action, for the rejection, then it can be positive, imaginary, can be negative, imaginary. We will choose the imaginary part, which is positive, then make the real part in the exponent is negative.

246
00:48:17.110 --> 00:48:21.200
Dongxue Qu: which means we want this integration. It's stable.

247
00:48:21.330 --> 00:48:28.489
Dongxue Qu: So here, in the end, even for the light cone, irregular configuration. We still want to choose. Some

248
00:48:28.500 --> 00:48:32.239
Dongxue Qu: choose the side of the branch cut, which is stable.

249
00:48:33.350 --> 00:48:34.580
Dongxue Qu: Okay.

250
00:48:34.580 --> 00:48:36.800
Florida Atlantic U: Okay, good. Thank you. That's all. All my questions.

251
00:48:42.800 --> 00:48:43.970
Hal Haggard: Seth, please.

252
00:48:45.246 --> 00:48:51.670
Seth Asante: Okay, hello. Thank you for a nice talk. I was just wondering in the 4 D case.

253
00:48:51.840 --> 00:48:57.969
Seth Asante: did the finiteness results also depend on a measure you choose for the path, integral or.

254
00:48:58.693 --> 00:49:04.480
Dongxue Qu: You mean the finite the 40 case. In the end, we have the

255
00:49:06.250 --> 00:49:10.360
Dongxue Qu: expectation value, the final expectation. Value one. Yeah.

256
00:49:10.695 --> 00:49:15.720
Seth Asante: Okay, I see. So you can also choose arbitrarily like measure for the length and.

257
00:49:17.044 --> 00:49:24.950
Dongxue Qu: Which is the la the expectation value for the aperture power or the lens. Yes.

258
00:49:25.390 --> 00:49:32.940
Dongxue Qu: and here actually find out if the power is larger enough, then these 2 match the

259
00:49:33.080 --> 00:49:34.090
Dongxue Qu: better.

260
00:49:34.600 --> 00:49:36.050
Seth Asante: Okay. Yes.

261
00:49:36.050 --> 00:49:36.690
Dongxue Qu: Hmm.

262
00:49:37.250 --> 00:49:38.150
Seth Asante: Thanks.

263
00:49:44.490 --> 00:49:47.379
Hal Haggard: Eugenio has one. He's getting to the microphone.

264
00:49:47.620 --> 00:49:56.560
UP: Whitmore 320: Yes. Microphone. Yeah, this is very nice. I can you, can you summarize a point in reverse by

265
00:49:56.900 --> 00:50:13.749
UP: Whitmore 320: suppose that by using the measure. You forbid a class of configurations just in identifying them by causal structure? Is there a choice that would make the path integral, always finite? What is it that you should excise

266
00:50:13.840 --> 00:50:17.049
UP: Whitmore 320: or remove to have always a fine result?

267
00:50:17.300 --> 00:50:19.000
UP: Whitmore 320: It doesn't make sense, it.

268
00:50:19.270 --> 00:50:45.379
Dongxue Qu: Yes, I think so. So. We always make a selection in the end. So we want make this integration finite. So we have to choose one set which makes the expectation value. All the partition function is finite. So basically, that's the whole point for our study. In the end, we need to make a selection, make a choice.

269
00:50:46.430 --> 00:50:57.468
UP: Whitmore 320: So suppose that you take the action as you started with this one that you see today. Yes, and you allow only

270
00:50:57.970 --> 00:50:59.310
Dongxue Qu: Only the

271
00:51:01.424 --> 00:51:10.540
Dongxue Qu: so in the end because the conventions we choose, you can see it's E to the power on I times S.

272
00:51:10.700 --> 00:51:20.109
Dongxue Qu: So it means. If it's Lawrence. In case, then they hope the imaginary part of the action should be greater than 0,

273
00:51:20.270 --> 00:51:26.729
Dongxue Qu: then it's the real part of the exponent will be negative.

274
00:51:27.700 --> 00:51:32.089
Dongxue Qu: So we will choose this set to do the computation

275
00:51:33.450 --> 00:51:34.300
Dongxue Qu: in that.

276
00:51:34.300 --> 00:51:37.846
UP: Whitmore 320: Do you see divergencies in the case where

277
00:51:38.410 --> 00:51:42.080
UP: Whitmore 320: The edges are assumed to be all space like

278
00:51:42.930 --> 00:51:44.170
UP: Whitmore 320: in the Lorentzian.

279
00:51:44.830 --> 00:51:46.479
Dongxue Qu: In the Laurentian case.

280
00:51:47.627 --> 00:51:49.419
Dongxue Qu: For for the

281
00:51:53.600 --> 00:51:56.809
Dongxue Qu: if we choose the one.

282
00:51:57.200 --> 00:52:01.479
Dongxue Qu: So let's 1st look at the action, if all the

283
00:52:01.890 --> 00:52:07.259
Dongxue Qu: so this is the case. If for all the bucket are space like.

284
00:52:07.670 --> 00:52:13.119
Dongxue Qu: then you can see, the action will depend on the boundary.

285
00:52:13.220 --> 00:52:15.149
Dongxue Qu: The boundary is 3D

286
00:52:15.400 --> 00:52:16.530
Dongxue Qu: geometry.

287
00:52:17.940 --> 00:52:24.500
Dongxue Qu: then actually, we are not sure this part is pretty imaginary at all.

288
00:52:24.510 --> 00:52:26.630
Dongxue Qu: all complex.

289
00:52:27.200 --> 00:52:30.630
Dongxue Qu: So it will depends on the boundary deficit angles.

290
00:52:32.640 --> 00:52:41.630
Dongxue Qu: Then basically, we need to choose a configuration which is the whose boundary geometry is nice enough.

291
00:52:41.960 --> 00:52:44.450
Dongxue Qu: then we have the finite result.

292
00:52:44.800 --> 00:52:50.380
Dongxue Qu: So from the this case I will see, it depends on the boundary.

293
00:52:51.210 --> 00:52:53.160
Dongxue Qu: It's finite or not.

294
00:52:55.430 --> 00:52:57.190
UP: Whitmore 320: Good. This is very helpful. Thank you.

295
00:52:57.190 --> 00:52:57.950
Dongxue Qu: Thank you.

296
00:52:58.730 --> 00:53:05.200
Hal Haggard: Dongshu, can I build on that question? Correct me if I'm wrong? But

297
00:53:05.390 --> 00:53:20.199
Hal Haggard: I understand that there's a slight tension in the light cone. Irregular case between the suppression that you're speaking about and correctly reproducing, for example, Black Hole entropy or entropy calculations.

298
00:53:20.650 --> 00:53:35.379
Hal Haggard: In one case you have to choose sort of the plus I and the other to get the correct entropy you have to choose the minus I. So my understanding and please, I'm not positive about this, but my understanding was that

299
00:53:35.390 --> 00:53:49.150
Hal Haggard: we need a physical criterion on when we should use 1 1 sign versus the other for the to get the physics right in different circumstances, and we don't really have that criterion right.

300
00:53:49.150 --> 00:53:54.290
Dongxue Qu: Yes, you are right. So I discussed this with Bianca, and for this study.

301
00:53:54.440 --> 00:54:08.850
Dongxue Qu: because we only care about the finiteness of the pass integral. So we adapted this kind of criteria for the for which, then, we choose for the action, for the imaginary part of the action.

302
00:54:08.890 --> 00:54:11.710
Dongxue Qu: but for the entropy. I think

303
00:54:11.810 --> 00:54:18.479
Dongxue Qu: they have some they don't have. They don't have some criteria about the

304
00:54:19.080 --> 00:54:20.020
Dongxue Qu: choice.

305
00:54:22.440 --> 00:54:27.749
Dongxue Qu: I'm not sure for the what's the physical meaning for that

306
00:54:29.730 --> 00:54:38.410
Dongxue Qu: But I think, Bianca, talk about this with Ted Jacobson about this a lot, and

307
00:54:38.420 --> 00:54:41.570
Dongxue Qu: till now they don't have any

308
00:54:41.680 --> 00:54:47.819
Dongxue Qu: conclusion till now. It's still an open question, and they are working on it.

309
00:54:48.550 --> 00:54:55.159
Hal Haggard: So I find that a really interesting subtlety, Eugenio, for how are we have to kind of?

310
00:54:55.190 --> 00:54:57.030
Hal Haggard: We have to find a criterion for.

311
00:54:57.030 --> 00:54:57.450
Dongxue Qu: Right.

312
00:54:57.450 --> 00:55:00.440
Hal Haggard: And we want one type of behavior versus another.

313
00:55:00.440 --> 00:55:05.277
Dongxue Qu: Yes, I agree, and it's a open question, and we will do it.

314
00:55:08.470 --> 00:55:11.130
Hal Haggard: Are there further comments or questions?

315
00:55:17.580 --> 00:55:21.059
Hal Haggard: All right? If not, let's thank Dongshu one more time. Thank you so much.

316
00:55:21.060 --> 00:55:22.690
Dongxue Qu: Thank you. Thank you.