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[λ] 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 λ. The propagator and the boundary two-point functions are derived for black hole solutions in hs[λ] × hs[λ] 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 W∞[ λ] symmetry and is deformed by higher-spin currents.