Boundary Conditions and Partition Functions in Higher Spin AdS${}_3$/CFT${}_2$

Abstract

We discuss alternative definitions of the semiclassical partition function in two-dimensional CFTs with higher spin symmetry, in the presence of sources for the higher spin currents. Theories of this type can often be described via Hamiltonian reduction of current algebras, and a holographic description in terms of three-dimensional Chern-Simons theory with generalized AdS boundary conditions becomes available. By studying the CFT Ward identities in the presence of non-trivial sources, we determine the appropriate choice of boundary terms and boundary conditions in Chern-Simons theory for the various types of partition functions considered. In particular, we compare the Chern-Simons description of deformations of the field theory Hamiltonian versus those encoding deformations of the CFT action. Our analysis clarifies various issues and confusions that have permeated the literature on this subject.

42 pages + appendices

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• Generalized Black Holes in Three-dimensional Spacetime
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• Higher spin entanglement entropy from CFT
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• Higher Spin Black Holes with Soft Hair
• Charged structure constants from modularity
• Warped Weyl fermion partition functions
• Holographic conformal blocks from interacting Wilson lines
• Comments on Thermalization in 2D CFT
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• Warped Black Holes in Lower-Spin Gravity
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• Higher spin entanglement entropy at finite temperature with chemical potential
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Higher-spin gauge theories in three spacetime dimensions
• The covariant action of higher spin black holes in three dimensions
• On the Explicit Asymptotic ${\mathcal{W}}_5$ Symmetry of 3D Chern-Simons Higher Spin $Ad{S}_3$ Gravity
• Unravelling Holographic Entanglement Entropy in Higher Spin Theories
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• 3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction
• Holographic chiral induced W-gravities
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter