On the partition functions of higher spin black holes

Abstract

We reconsider black hole solutions of D = 3 higher-spin gravity in the $hs[\lambda ]\oplus hs[\lambda ]$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential $\alpha$, and non-zero values of all the conserved charges associated with the asymptotic ${\mathcal{W}}_{\infty }[\lambda ]$ symmetry. We extend the available perturbative expansion of the partition function to order $\mathcal{O}({\alpha }^{18})$ for generic values of the $\lambda$ parameter. The result matches the CFT prediction at $\lambda =0$ and at $\lambda =1$ where we provide the exact all-order expansion of the partition function. The perturbative series is then analysed in the interesting non-trivial limit $\lambda \to \infty$ and we derive the exact analytical expressions of the partition function and the spin-4 charge in closed form as functions of $\alpha$. Also, the first subleading correction at large $\lambda$ is shown to be simply related to the leading contribution.

15 pages, 4 figures. v2: more comments and references

References in corpus (1)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

Cited by in corpus (10)

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• Analysis of higher spin black holes with spin-4 chemical potential
• Aspects of Higher-Spin Theory with Fermions
• Resummation of scalar correlator in higher spin black hole background
• Relative entropy in higher spin holography
• Renyi divergences from Euclidean quenches
• Phase Structure of Higher Spin Black Holes