Partition functions of higher spin black holes and their CFT duals

TL;DR

This paper constructs higher-spin black hole solutions in three-dimensional gravity, computes their partition functions with chemical potentials, and confirms the duality with boundary CFTs at specific parameters, supporting the higher-spin holography conjecture.

Contribution

It provides explicit higher-spin black hole solutions, calculates their partition functions perturbatively, and verifies the duality with boundary CFTs at special values of the parameter.

Findings

Partition functions match boundary CFT computations at  and 1.

Explicit higher-spin black hole solutions are constructed.

Results support the higher-spin holography conjecture for generic .

Abstract

We find black hole solutions of D=3 higher-spin gravity in the hs[\lambda] + hs[\lambda] Chern-Simons formulation. These solutions have a spin-3 chemical potential, and carry nonzero values for an infinite number of charges of the asymptotic W_{\infty}[\lambda] symmetry. Applying a previously developed set of rules for ensuring smooth solutions, we compute the black hole partition function perturbatively in the chemical potential. At \lambda =0, 1 we compare our result against boundary CFT computations involving free bosons and fermions, and find perfect agreement. For generic \lambda\ we expect that our gravity result will match the partition function of the coset CFTs conjectured by Gaberdiel and Gopakumar to be dual to these bulk theories.