The Holographic Ward identity: Examples from 2+1 gravity

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.

arXiv comment13 pages, no figures, plain Latex

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Cited by in corpus (21)

• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Higher Spin Black Holes
• Scalar fields and three-point functions in D=3 higher spin gravity
• Stress tensor correlators in three-dimensional gravity
• The action for higher spin black holes in three dimensions
• Horizon fluff, semi-classical black hole microstates - Log-corrections to BTZ entropy and black hole/particle correspondence
• Observables and Microscopic Entropy of Higher Spin Black Holes
• Probing higher spin black holes from CFT
• Holographic currents in first order Gravity and finite Fefferman-Graham expansions
• Boundary Conditions and Partition Functions in Higher Spin AdS${}_3$/CFT${}_2$
• Three-Point Functions in N=2 Higher-Spin Holography
• Warped Black Holes in Lower-Spin Gravity
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• Holographic boundary actions in AdS${}_3$/CFT${}_2$ revisited
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• The covariant action of higher spin black holes in three dimensions
• Two dimensional RG flows and Yang-Mills instantons
• Holographic chiral induced W-gravities
• DC conductance and memory in 3D gravity
• Holographic Duality for 3D Spin-3 Gravity Coupled to Scalar Field