On scalar propagators of three-dimensional higher-spin black holes

Abstract

We explore some aspects of three-dimensional higher-spin holography by studying scalar fluctuations in the background of higher-spin black holes. We furnish an independent derivation of the bulk-boundary propagator by purely invoking a well-known infinite dimensional matrix representation of $hs[\lambda ]$ algebra related to its construction as a quotient of the universal enveloping algebra of $sl(2)$, thus evading the need in previous literature to perform an analytic continuation from some integer to $\lambda$. The propagator and the boundary two-point functions are derived for black hole solutions in $hs[\lambda ]\times hs[\lambda ]$ Chern-Simons theory with spin-3 and spin-4 charges up to second-order in the potentials. We match them with three- and four-point torus correlation functions of the putative dual conformal field theory which has ${\mathcal{W}}_{\infty }[\lambda ]$ symmetry and is deformed by higher-spin currents.

arXiv comment27 pages. v3: references added

References in corpus (37)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• An AdS_3 Dual for Minimal Model CFTs
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Measurement of $J/\psi$ helicity distributions in inelastic photoproduction at HERA
• Minimal Model Holography
• Symmetries of Holographic Minimal Models
• Higher Spin Black Holes
• Black holes in three dimensional higher spin gravity: A review
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Triality in Minimal Model Holography
• Scaled momentum distributions of charged particles in dijet photoproduction at HERA
• Higher Spin Black Holes from CFT
• Partition Functions of Holographic Minimal Models
• Higher spin AdS_3 supergravity and its dual CFT
• Generalized Black Holes in Three-dimensional Spacetime
• Partition functions of higher spin black holes and their CFT duals
• Thermodynamics of Higher Spin Black Holes in AdS${}_3$
• Scalar fields and three-point functions in D=3 higher spin gravity
• Thermodynamics of higher spin black holes in 3D
• Higher spin black hole entropy in three dimensions
• Chiral Deformations of Conformal Field Theories
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Aspects of Three-dimensional Spin-4 Gravity
• Holographic conformal blocks from interacting Wilson lines
• Matching four-point functions in higher spin AdS_3/CFT_2
• Probing higher spin black holes from CFT
• Probing higher spin black holes
• Exploring Three-dimensional Higher-Spin Supergravity based on sl(N |N - 1) Chern-Simons theories
• A note on conical solutions in 3D Vasiliev theory
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• Black holes in higher spin supergravity
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Analysis of higher spin black holes with spin-4 chemical potential
• Resummation of scalar correlator in higher spin black hole background

Cited by in corpus (1)

• Higher-spin gauge theories in three spacetime dimensions