String Theory on Warped AdS_3 and Virasoro Resonances

TL;DR

This work analyzes holography for time-like warped AdS$_3$ in string theory by leveraging exact worldsheet CFT descriptions and a supergravity perspective to identify spacetime Virasoro symmetries. The authors show that a universal spacetime Virasoro algebra with central charge $c_{\mathrm{st}}=6k|w|$ arises, and that a second commuting Virasoro algebra can appear on a dense set of moduli when the deformation parameters meet a rationality condition, with central charges $c_{\mathrm{st}}=6k(\rho w+\mu \omega)$ and $\bar{c}_{\mathrm{st}}=6k|w|$. They extend the analysis to heterotic and Type II strings, study spacetime supersymmetry under the deformation, and perform a Brown–Henneaux-type asymptotic-symmetry analysis in supergravity that supports the worldsheet results, including enhanced symmetry cases with $c_{st}=\bar{c}_{st}=3\ell\sqrt{1+2\textsc{h}^2}/(2G_3)$. The discussion addresses dual CFT interpretations, modular-invariance caveats, and open questions about brane realizations and extensions to spacelike/null warped AdS$_3$ geometries. Overall, the paper builds a detailed bridge between exact worldsheet constructions and spacetime symmetry structures in warped AdS$_3$ backgrounds, informing holography beyond AdS.

Abstract

We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include Gödel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis.