Abstract
We propose a set of boundary terms for higher spin theories in AdS3 that lead to a well-defined variational principle compatible with Dirichlet boundary conditions for the metric and higher spin fields. These boundary terms are valid for higher spin theories in the Fefferman-Graham gauge and they allow us to compute the canonical free energy of higher spin black holes directly from the Euclidean, covariant, on-shell action. Using these results we reproduce the thermodynamics of the higher spin black hole of Ammon, Gutperle, Kraus, and Perlmutter and comment on the corresponding theory of induced \( \mathcal{W} \)-gravity at the boundary.
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Apolo, L. The covariant action of higher spin black holes in three dimensions. J. High Energ. Phys. 2016, 97 (2016). https://doi.org/10.1007/JHEP05(2016)097
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DOI: https://doi.org/10.1007/JHEP05(2016)097