Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence

TL;DR

This paper investigates the asymptotic symmetries in the TsT/$Tar T$ holographic correspondence, revealing a non-local field redefinition that relates the symmetries before and after the transformation, aligning string theory and field theory results.

Contribution

It demonstrates a state-dependent, non-local field redefinition that maps the string theory's asymptotic symmetries under TsT transformation to the original form, clarifying the holographic duality.

Findings

Asymptotic symmetry in the auxiliary AdS basis is generated by two Virasoro algebras.

In the TsT transformed basis, the symmetry algebra becomes non-linear and non-local.

The string theory analysis aligns with the $Tar T$ deformed CFT$_2$ results.

Abstract

Starting from holography for IIB string theory on AdS$_3\times \mathcal N$ with NS-NS flux, the TsT/$T\bar T$ correspondence is a conjecture that a TsT transformation on the string theory side is holographically dual to the single-trace version of the $T\bar T$ deformation on the field theory side. More precisely, the long string sector of string theory on the TsT-transformed background corresponds to the symmetric product theory whose seed theory is the $T\bar T$-deformed CFT$_2$. In this paper, we study the asymptotic symmetry of the string theory in the bulk. We find a state-dependent, non-local field redefinition under which the worldsheet equations of motion, stress tensor, as well as the symplectic form of string theory after the TsT transformation are mapped to those before the TsT transformation. The asymptotic symmetry in the auxiliary AdS basis is generated by two commuting Virasoro generators, while in the TsT transformed basis is non-linear and non-local. Our result from string theory analysis is compatible with that of the $T\bar T$ deformed CFT$_2$.