The Spectrum of Strings on Warped AdS_3 x S^3

TL;DR

This work analyzes a TsT-induced, null-w warped deformation of string theory on $AdS_3\times S^3$, breaking part of the spacetime symmetry while preserving a right-moving Virasoro-Kac-Moody structure and a global left $U(1)_L\times SU(2)_L$. Using a nonlocal field redefinition, the authors map the deformed worldsheet theory to the undeformed model with twisted boundary conditions, enabling an exact spectral-flow-based determination of the massive string spectrum. They derive explicit expressions for the deformed spectrum, show agreement with supergravity in the appropriate limit, and examine the fate of boundary modes, including gravitons and gluons, under the deformation. The paper also discusses crossover Kac-Moody structures and their potential realization via boundary conditions, as well as finite-temperature extensions to warped black strings and their entropy properties. Overall, the results illuminate how nonlocal deformations reshape the string spectrum and boundary dynamics in warped holographic settings, offering a concrete bridge between worldsheet techniques and warped AdS/CFT phenomenology.

Abstract

String theory on NS-NS AdS_3 x S^3 admits an exactly marginal deformation which breaks the SL(2,R)_R x SL(2,R)_L isometry of AdS_3 down to SL(2,R)_R x U(1)_L. The holographic dual is an exotic and only partially understood type of two-dimensional CFT with a reduced unbroken global conformal symmetry group. In this paper we study the deformed theory on the string worldsheet. It is found to be related by a spectral flow which is nonlocal in spacetime to the undeformed worldsheet theory. An exact formula for the spectrum of massive strings is presented.