$\frac{SL(2,\mathbb{R})\times U(1)}{U(1)}$ CFT, NS5$+$F1 system and single trace $T\bar{T}$

TL;DR

This paper establishes the equivalence between a specific worldsheet string theory, the near horizon NS5 brane system, and a single trace $T\bar{T}$ deformation of string theory in $AdS_3$, providing spectrum and correlation function matches.

Contribution

It proves the equivalence among the coset sigma model, NS5 brane near horizon theory, and single trace $T\bar{T}$ deformation of string theory in $AdS_3$, with explicit spectrum and correlator computations.

Findings

Spectrum matches between BRST quantization and $T\bar{T}$ deformed theory.

Two-point functions agree with supergravity calculations.

Confirmed the equivalence through explicit worldsheet and spacetime analysis.

Abstract

In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model $\frac{SL(2,\mathbb{R})_k\times U(1)}{U(1)}\times S^3 \times T^4$ with $SL(2,\mathbb{R})$ WZW level $k\geq 2$, (ii) the full near horizon theory of the NS5 branes with $k$ NS5 branes wrapping $T^4\times S^1$, $p\gg1$ F1 strings wrapping $S^1$ and $n$ units of momentum along the $S^1$ and (iii) the single trace $T\bar{T}$ deformation of string theory in $AdS_3\times S^3\times T^4$. As a check we compute the spectrum of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace $T\bar{T}$ deformed string theory in $AdS_3$. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach.