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The covariant action of higher spin black holes in three dimensions
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abstract
We propose a set of boundary terms for higher spin theories in AdS$_3$ 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 $\cal{W}$-gravity at the boundary.
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On topological defects in Chern-Simons theory
R-matrix solutions of the modified classical Yang-Baxter equation define non-invertible topological surface defects in non-Abelian Chern-Simons theory, with semigroup fusion.
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