Partition functions of higher spin black holes and their CFT duals
arXiv:1108.2567 · doi:10.1007/JHEP11(2011)061
Abstract
We find black hole solutions of D=3 higher-spin gravity in the hs[λ] + hs[λ] 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}[λ] 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 λ=0, 1 we compare our result against boundary CFT computations involving free bosons and fermions, and find perfect agreement. For generic λ 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.
28 pages; v2, added ref