Probing higher spin black holes

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.