Critical points of warped AdS/CFT and higher-curvature gravity

Warped anti-de Sitter (WAdS)/warped conformal field theory (WCFT) correspondence is an interesting realization of non-AdS holography. It relates three-dimensional warped anti-de Sitter (${\mathrm{WAdS}}_3$) spaces to a special class of two-dimensional quantum field theory with chiral scaling symmetry that acts only on right-moving modes. The latter are often called warped conformal field theories (${\mathrm{WCFT}}_2$), and their existence makes WAdS/WCFT particularly interesting as a tool to investigate a new type of two-dimensional conformal structure. Besides, WAdS/WCFT is interesting because it enables one to apply holographic techniques to the microstate counting problem of non-AdS, nonsupersymmetric black holes. Asymptotically ${\mathrm{WAdS}}_3$ black holes (${\mathrm{WBH}}_3$) appear as solutions of topologically massive theories, Chern-Simons theories, and many other models. Here, we explore ${\mathrm{WBH}}_3\times {\mathrm{\Sigma }}_{D-3}$ solutions of $D$-dimensional higher-curvature gravity, with ${\mathrm{\Sigma }}_{D-3}$ 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 ${\text{WAdS}}_3\times {\mathrm{\Sigma }}_{D-3}$ vacua are the squashed/stretched analogs of the ${\mathrm{AdS}}_D$ Chern-Simons point of Lovelock gravity.