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.

27 pages. v3: references added

References in corpus (5)

• 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
• Symmetries of Holographic Minimal Models
• Generalized Black Holes in Three-dimensional Spacetime
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes

Cited by in corpus (1)

• Higher-spin gauge theories in three spacetime dimensions