Multi-centered AdS3 solutions from Virasoro conformal blocks

113

Abstract:We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal t − 3 2 power-law decay. For the vacuum block the transition occurs at t ≈ πc 6h L , confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the 'forbidden singularities'. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.

“…Moreover, these problems can be partially addressed by performing explicit analytic calculations [7]. The blocks can also be computed directly from AdS 3 [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A numerical approach to Virasoro blocks and the information paradox

Chen

Hussong

Kaplan

et al. 2017

113

“…As rather elegantly proved in [29], this property implies that in general the monodromy matrix M is up to a similarity transformation contained within the group SU(1, 1). Since similarity transformation do not effect the eigenvalues this restricts the eigenvalues of M to be either pure phase or purely real (see figure 3).…”

Section: Jhep08(2018)047mentioning

confidence: 92%

“…As mentioned in a previous section, in [29] it was shown that these constraints imply the reflection symmetry z 2 T (z) = 1 z 2T (1/z). In the following section we will assume that the insertions are evenly distributed around the circle.…”

Section: Jhep08(2018)047mentioning

confidence: 94%

“…Given the reflection property of the Fuchs equation, the following JHEP08(2018)047 two monodromy problems are equivalent; either one fixes the accessory parameters such that the monodromy around a mirror pair is trivial or one fixes the accessory parameters such that any cycle around a single regular singular point yields a monodromy that falls within SU (1,1). Given the reflection property of T (z) it was shown in [29] that there exists a basis of solutions with the property that their ratio satisfies the same reflection property. From this, combined with the conjugacy class of M being contained within SU(1, 1) it was shown that the monodromy of this pair of solutions around a mirror pair is trivial.…”

Section: Colliding N Clusters To Form a Black Holementioning

confidence: 99%

“…Since the monodromy is a basis independent property this concluded the proof that the monodromy around a mirror pair is trivial. For an extensive proof of this statement we refer to [29]. This demand fully determines the irregular part of the stress tensor and hence it is a well-defined problem to compute the monodromy around the unit circle.…”

Section: Colliding N Clusters To Form a Black Holementioning

confidence: 99%

See 2 more Smart Citations

On the universality of late-time correlators in semi-classical 2d CFTs

Banerjee

Bryan

Vos

2018

In the framework of the AdS 3 / CFT 2 correspondence, we present a systematic analysis of the late time thermalization of a two dimensional CFT state created by insertion of small number of heavy operators on the vacuum. We show that at late Lorentzian time, the universal features of this thermalization are solely captured by the eigenvalues of the monodromy matrix corresponding to the solutions of the uniformization equation. We discuss two different ways to extract the monodromy eigenvalues while bypassing the need for finding explicitly the full monodromy matrix -first, using a monodromy preserving diffeomorphism and second using Chen-Simons formulation of gravity in AdS 3 . Both of the methods yield the same precise relation between the eigenvalues and the final black hole temperature at late Lorentzian time.

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity

Kusuki

2019

120

The light cone OPE limit provides a significant amount of information regarding the conformal field theory (CFT), like the high-low temperature limit of the partition function. We started with the light cone bootstrap in the general CFT 2 with c > 1. For this purpose, we needed an explicit asymptotic form of the Virasoro conformal blocks in the limit z → 1, which was unknown until now. In this study, we computed it in general by studying the pole structure of the fusion matrix (or the crossing kernel). Applying this result to the light cone bootstrap, we obtained the universal total twist (or equivalently, the universal binding energy) of two particles at a large angular momentum. In particular, we found that the total twist is saturated by the value c−1 12 if the total Liouville momentum exceeds beyond the BTZ threshold. This might be interpreted as a black hole formation in AdS 3 .As another application of our light cone singularity, we studied the dynamics of entanglement after a global quench and found a Renyi phase transition as the replica number was varied. We also investigated the dynamics of the 2nd Renyi entropy after a local quench.We also provide a universal form of the Regge limit of the Virasoro conformal blocks from the analysis of the light cone singularity. This Regge limit is related to the general n-th Renyi entropy after a local quench and out of time ordered correlators. the OPE associativity.