A perturbative CFT dual for pure NS-NS AdS$_3$ strings

TL;DR

The paper builds a perturbative holographic dual for bosonic AdS$_3$ with pure NS-NS flux by proposing a grand-canonical symmetric orbifold CFT, Sym$^N$(R$_Q$ × X) deformed by a twist-2 operator in the linear-dilaton sector. By performing detailed conformal perturbation theory and matching to worldsheet calculations, it shows agreement of two- and three-point functions up to fourth order in the deformation parameter and demonstrates that both short- and long-string spectra align across the dual descriptions. The analysis hinges on a sophisticated use of covering-space technology, KPZ scaling, and pole structure in correlators to access discrete states, while also addressing large-$N$ and genus-zero limitations and extending the framework to superstrings. The results provide compelling evidence for a perturbative duality in $N^{-1}$, with rich implications for nonperturbative definitions, discrete spectra, and potential connections to topological formulas and matrix-string ideas. The work lays a groundwork for further nonperturbative formulations and higher-genus tests in AdS$_3$/CFT$_2$ with NS-NS flux.

Abstract

We construct a CFT dual to string theory on AdS$_3$ with pure NS-NS flux. It is given by a symmetric orbifold of a linear dilaton theory deformed by a marginal operator from the twist-2 sector. We compute two- and three-point functions on the CFT side to 4th order in conformal perturbation theory at large $N$. They agree with the string computation at genus 0, thus providing ample evidence for a duality. We also show that the full spectra of both short and long strings on the CFT and the string side match. The duality should be understood as perturbative in $N^{-1}$.