Hopfing and Puffing Warped Anti-de Sitter Space

TL;DR

The paper investigates 3D spacelike warped AdS$_3$ geometries in Einstein gravity without a gravitational Chern-Simons term and proposes a holographic dual CFT with equal left and right central charges $c_L=c_R=\frac{\sqrt{3}\,(4-\beta^2)^{1/2}\,\beta\,\ell}{2G_3}$, derived from Bekenstein-Hawking entropies of warped black holes and warped self-dual solutions. It demonstrates that these central charges reproduce the Cardy-form entropy for warped BHs and self-dual states, and uses Hopf T-duality to relate the dual CFTs of AdS$_3\times S^3$ and warped AdS$_3\times S^3$ near-horizons in six dimensions. The authors then apply the central charges to the entropy of Hopf T-dualized six-dimensional black strings, showing that Hopf T-duality maps thermal states with equal entropy in the dual CFTs, consistent with horizon-area invariance. The work also analyzes duality chains along different fiber directions, highlighting how central charges transform and how entropies match across dual descriptions, and discusses implications for extremal Kerr and AdS$_2$ limits, along with remaining open questions about ASG formulations and brane realizations.

Abstract

Three dimensional spacelike warped anti-de Sitter space is studied in the context of Einstein theories of gravity and string theory, where there is no gravitational Chern-Simons term in the action. We propose that it is holographically dual to a two-dimensional conformal field theory with equal left and right moving central charges. Various checks of the central charges are offered, based on the Bekenstein-Hawking entropy of the stretched warped black holes and warped self-dual solutions. The proposed central charges are applied to compute the Bekenstein-Hawking entropy of the Hopf T-dual of six-dimensional dyonic black strings which have a near horizon consisting of three dimensional warped anti-de Sitter space times a three-sphere. We find that the Hopf T-duality is a map between thermal states with equal entropy of the CFTs dual to the dyonic black string and the Hopf T-dualized black string.