Hopfing and Puffing Warped Anti-de Sitter Space

TL;DR

This paper explores the holographic duality between three-dimensional warped anti-de Sitter space and two-dimensional conformal field theories, providing checks via black hole entropy and applying T-duality to relate different black string solutions.

Contribution

It proposes a holographic duality for warped AdS space with equal left and right central charges, supported by entropy calculations and T-duality analysis.

Findings

Central charges are equal for the dual CFTs.

Black hole entropy matches CFT predictions.

Hopf T-duality relates entropies of dual black strings.

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.