Higher-curvature gravity in AdS$_3$, holographic $c$-theorems and black hole microstates

We construct higher-derivative gravity theories in three dimensions that admit holographic $c$-theorems and exhibit a unique maximally symmetric vacuum, at arbitrary order $n$ in the curvature. We show that these theories exhibit special properties, the most salient ones being the decoupling of ghost modes around Anti-de Sitter (AdS) space, the enhancement of symmetries at linearized level, and the existence of a one-parameter generalization of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole that, while being asymptotically AdS, is not of constant curvature but rather exhibits a curvature singularity. For such black holes, we provide a holographic derivation of their thermodynamics. This gives a microscopic picture of black hole thermodynamics for non-supersymmetric solutions, of non-constant curvature in higher-derivative theories of arbitrary order in the curvature.