$T\bar{T}$ deformations as TsT transformations

TL;DR

This paper explores the geometric interpretation of $T\bar{T}$ deformations as TsT transformations, linking gauge choices, T-duality, and worldsheet S-matrix modifications in string theory backgrounds.

Contribution

It establishes a novel geometric perspective of $T\bar{T}$ deformations as TsT transformations, connecting gauge fixing, T-duality, and S-matrix twists in string theory.

Findings

$T\bar{T}$ deformations correspond to TsT transformations involving light-cone coordinates.

The $T\bar{T}$ CDD factor is interpreted as a Drinfel'd-Reshetikhin twist of the S matrix.

Explicit geometries for deformed pp-wave and LLM backgrounds are constructed.

Abstract

The relationship between $T\bar{T}$ deformations and the uniform light-cone gauge, first noted in arXiv:1804.01998, provides a powerful generating technique for deformed models. We recall this construction, distinguishing between changes of the gauge frame, which do not affect the theory, and genuine deformations. We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing. Exploiting a formal relation between uniform light-cone gauge and static gauge in a T-dual frame, we interpret such a change as a TsT transformation involving the two light-cone coordinates. In the static-gauge picture, the $T\bar{T}$ CDD factor then has a natural interpretation as a Drinfel'd-Reshetikhin twist of the worldsheet S matrix. To illustrate these ideas, we find the geometries yielding a $T\bar{T}$ deformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds.