Conformal blocks beyond the semi-classical limit

Abstract:We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.

Section: Finding Redshift In Gravitymentioning

confidence: 99%

“…In [41] an explicit model of shell collapse was studied, using the methods of [34][35][36][37]. The shell was represented by a number of infalling particles in the gravity description, and a…”

Section: Finding Redshift In Gravitymentioning

confidence: 99%

One-loop transition amplitudes in the D1D5 CFT

Carson

Hampton

Mathur

2017

“…It would be interesting to generalize our results to black-hole-like extremal solutions where one allows also singularities of parabolic or hyperbolic type. 10 • It would be interesting to generalize our results to 3D higher spin gravity, relating multi-centered higher spin solutions to W -algebra conformal blocks [55]. Since massless higher spin fields are most simply formulated in terms of Chern-Simons fields, this would involve a generalization of the Chern-Simons description of our solutions discussed at the end of section 4.…”

Section: Jhep03(2017)129mentioning

confidence: 99%

“…Recent investigations have focused on the important question of how local physics in the bulk is encoded in properties of the dual CFT. Natural localized objects to study holographically are line defects arising from adding point particles to the bulk, which have recently been shown to be intimately linked to conformal blocks in the dual CFT [2][3][4][5] (related work appears in [6][7][8][9][10][11][12][13][14][15][16][17]). In the case of AdS 3 , which we will focus on in this paper, it was shown that Virasoro conformal blocks at large central charge can be computed from the action of configurations of point particles in the bulk AdS 3 .…”

Section: Introductionmentioning

confidence: 99%

Multi-centered AdS3 solutions from Virasoro conformal blocks

Hulík

Procházka²,

Raeymaekers

2017

Abstract:We revisit the construction of multi-centered solutions in three-dimensional anti-de Sitter gravity in the light of the recently discovered connection between particle worldlines and classical Virasoro conformal blocks. We focus on multi-centered solutions which represent the backreaction of point masses moving on helical geodesics in global AdS 3 , and argue that their construction reduces to a problem in Liouville theory on the disk with Zamolodchikov-Zamolodchikov boundary condition. In order to construct the solution one needs to solve a certain monodromy problem which we argue is solved by a vacuum classical conformal block on the sphere in a particular channel. In this way we construct multi-centered gravity solutions by using conformal blocks special functions. We show that our solutions represent left-right asymmetric configurations of operator insertions in the dual CFT. We also provide a check of our arguments in an example and comment on other types of solutions.

“…The essence is that the presence of the heavy operators change the background geometry to a BTZ black hole. For other aspects on this type of conformal block, see [27][28][29][30][31].…”

Section: Jhep10(2016)110mentioning

confidence: 99%

Holographic description of 2D conformal block in semi-classical limit

Chen

Zhang

2016

Abstract:In this paper, we study the holographic descriptions of the conformal block of heavy operators in two-dimensional large c conformal field theory. We consider the case that the operators are pairwise inserted such that the distance between the operators in a pair is much smaller than the others. In this case, each pair of heavy operators creates a conical defect in the bulk. We propose that the conformal block is dual to the on-shell action of three dimensional geometry with conical defects in the semi-classical limit. We show that the variation of the on-shell action with respect to the conical angle is equal to the length of the corresponding conical defect. We derive this differential relation on the conformal block in the field theory by introducing two extra light operators as both the probe and the perturbation. Our study also suggests that the area law of the holographic Rényi entropy must holds for a large class of states generated by a finite number of heavy operators insertion.