Minimal Log Gravity

Abstract

Minimal Massive Gravity (MMG) is an extension of three-dimensional Topologically Massive Gravity that, when formulated about Anti-de Sitter space, accomplishes to solve the tension between bulk and boundary unitarity that other models in three dimensions su§er from. We study this theory at the chiral point, i.e. at the point of the parameter space where one of the central charges of the dual conformal Öeld theory vanishes. We investigate the non-linear regime of the theory, meaning that we study exact solutions to the MMG Öeld equations that are not Einstein manifolds. We exhibit a large class of solutions of this type, which behave asymptotically in di§erent manners. In particular, we Önd analytic solutions that represent two-parameter deformations of extremal BaÒados-Teitelboim-Zanelli (BTZ) black holes. These geometries behave asymptotically as solutions of the so-called Log Gravity, and, despite the weakened falling-o§ close to the boundary, they have Önite mass and Önite angular momentum, which we compute. We also Önd time-dependent deformations of BTZ that obey Brown-Henneaux asymptotic boundary conditions. The existence of such solutions shows that Birkho§ theorem does not hold in MMG at the chiral point. Other peculiar features of the theory at the chiral point, such as the degeneracy it exhibits in the decoupling limit, are discussed.