Abstract
The bulk reconstructions in AdS/CFT and its cousins are essential to understand the holographic nature of quantum gravity. In this work, we try to study the bulk reconstruction in the AdS$_3$/WCFT$_2$ correspondence. After deriving the bulk-boundary propagator, which is different from the usual one in AdS/CFT, we define the bulk proto-scalar field by using the Virasoro-Kac-Moody symmetry in two different ways. One is to impose the bulk primary conditions on the field and construct the field algebraically. The other is to use the bulk-boundary vacuum OPE block, which can be read by applying the diffeomorphism preserving the CSS boundary conditions. Two approaches lead to consistent picture.
Highlights
The AdS/CFT correspondence states that the quantum gravity in anti–de Sitter (AdS) spacetime is dual to a conformal field theory at asymptotical AdS boundary [1]
We study the bulk reconstruction in the AdS3=WCFT2 correspondence
We focus on the bulk-boundary vacuum operator product expansion (OPE) block, which can be read from the diffeomorphism preserving the CSS boundary conditions and is most related to the bulk gravitational physics
Summary
The AdS/CFT correspondence states that the quantum gravity in anti–de Sitter (AdS) spacetime is dual to a conformal field theory at asymptotical AdS boundary [1]. One central question is to understand how the holography works in the correspondence This inspired people to study the holographic duality to the spacetime beyond the AdS or the quantum field theory without full conformal symmetry. It was proposed that the AdS3 gravity with CSS boundary conditions should be dual to a warped CFT, which has the same Virasoro-Kac-Moody symmetry [5] This socalled AdS3=WCFT2 correspondence has been studied from several points of view, including the microscopic entropy of black holes [11], the entanglement entropy [9,10,12], the one-loop partition function [13] and very recently the Renyi mutual information of two disjoint intervals [14].
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