The Holographic Ward identity: Examples from 2+1 gravity
Maximo Banados, Rodrigo Caro
TL;DR
This paper explores how boundary Ward identities in the AdS/CFT correspondence are represented in 2+1 gravity using Chern-Simons formulation, highlighting modifications needed for conformal and supersymmetric cases.
Contribution
It provides a detailed analysis of boundary Ward identities in 3D gravity, including modifications for conformal and supersymmetric identities within the Chern-Simons framework.
Findings
Derived necessary modifications to chiral currents for Virasoro operators
Analyzed supersymmetric Ward identities in 3D gravity
Clarified boundary conditions' impact on Ward identities
Abstract
In the AdS/CFT correspondence the boundary Ward identities are encoded in the bulk constraints. We study the three-dimensional version of this result using the Chern-Simons formulation of gravity. Due the metric boundary conditions the conformal identities cannot be derived in a straightforward way from the chiral ones. We pay special attention to this case and find the necessary modifications to the chiral currents in order to find the two Virasoro operators. The supersymmetric Ward identities are studied as well.
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