Critical points of WAdS/CFT and higher-curvature gravity

Abstract

WAdS/WCFT correspondence is an interesting realization of non-AdS holography. It relates 3-dimensional Warped-Anti-de Sitter (WAdS${}_3$) spaces to a special class of 2-dimensional quantum field theory with chiral scaling symmetry that acts only on right-moving modes. The latter are often called Warped Conformal Field Theories (WCFT${}_2$), and their existence makes WAdS/WCFT particularly interesting as a tool to investigate a new type of 2-dimensional conformal structure. Besides, WAdS/WCFT is interesting because it enables to apply holographic techniques to the microstate counting problem of non-AdS, non-supersymmetric black holes. Asymptotically WAdS${}_3$ black holes (WBH${}_3$) appear as solutions of topologically massive theories, Chern-Simons theories, and many other models. Here, we explore WBH${}_3\times {\Sigma }_{D-3}$ solutions of $D$-dimensional higher-curvature gravity, with ${\Sigma }_{D-3}$ being different internal manifolds, typically given by products of deformations of hyperbolic spaces, although we also consider warped products with time-dependent deformations. These geometries are solutions of the second order higher-curvature theory at special (critical) points of the parameter space, where the theory exhibits a sort of degeneracy. We argue that the dual (W)CFT at those points is actually trivial. In many respects, these critical points of WAdS${}_3\times {\Sigma }_{D-3}$ vacua are the squashed/stretched analogs of the AdS${}_D$ Chern-Simons point of Lovelock gravity.

arXiv comment14 pages

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