Probing higher spin black holes

TL;DR

This paper investigates scalar field propagation in three-dimensional higher spin gravity backgrounds, deriving bulk-boundary propagators, analyzing higher spin black holes, and exploring their thermal and causal properties.

Contribution

It provides a method to compute bulk-boundary propagators using group theory and higher spin symmetry, including explicit results for spin-3 deformations and black hole backgrounds.

Findings

Derived a closed-form propagator in spin-3 deformed AdS_3.

Proved propagator periodicity aligns with black hole thermality.

Computed propagator in higher spin black hole at first order in charge.

Abstract

We study the propagation of scalar fields on various backgrounds in three dimensional higher spin gravity. Our main emphasis is on obtaining the bulk-boundary propagator, which can be efficiently computed using group theory and higher spin gauge symmetry and from which we can extract scalar two-point functions in the dual CFT. As an illustration, we obtain a simple closed form expression for the propagator in a particular spin-3 deformation of AdS_3. In the case of higher spin black holes, we prove on general grounds that the propagator respects an imaginary time periodicity consistent with the thermal nature of the black hole; in doing so we make progress in understanding the group exponentiation of the higher spin Lie algebra hs[\lambda], and its center. We also explicitly compute the propagator in the black hole background at first order in the higher spin charge. Evaluated on the Lorentzian section, the result is consistent with an interpretation in which the black hole has two causally disconnected boundary components, as is the case for the BTZ black hole.