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

TL;DR

This paper investigates scalar fluctuations in three-dimensional higher-spin black hole backgrounds, deriving bulk-boundary propagators and correlating them with dual CFT predictions without analytic continuation, advancing higher-spin holography understanding.

Contribution

It provides an independent derivation of the bulk-boundary propagator using matrix representations of $hs[rac{]}$ algebra, avoiding analytic continuation, and matches bulk results with dual CFT correlators.

Findings

Derived scalar propagators for higher-spin black holes

Matched bulk correlators with dual CFT three- and four-point functions

Extended analysis to spin-3 and spin-4 charges up to second order

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.