Higher-curvature gravity in AdS3 , holographic c -theorems, and black hole microstates

We construct higher-derivative gravity theories in three dimensions that admit holographic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi></a:math>-theorems and exhibit a unique maximally symmetric vacuum, at arbitrary order <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>n</c:mi></c:math> 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 Bañados-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 nonsupersymmetric solutions, of nonconstant curvature in higher-derivative theories of arbitrary order in the curvature. Published by the American Physical Society 2024