T-Duality and $T \overline{T}$-like Deformations of Sigma Models

TL;DR

This paper explores how T-duality transformations interact with $T ar{T}$-like deformations in two-dimensional sigma models, showing they commute under certain conditions and preserving classical integrability.

Contribution

It demonstrates the commutation of T-duality with $T ar{T}$-like deformations in sigma models, including non-Abelian cases, and establishes their classical integrability.

Findings

Abelian T-duality commutes with $T ar{T}$ deformation.

Non-Abelian T-duality also commutes with $T ar{T}$-like flows.

Deformations preserve classical integrability of models.

Abstract

We initiate the study of the interplay between T-duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T-duality commutes with the $T \overline{T}$ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T-duality and arbitrary $T \overline{T}$-like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T-dual are classically integrable.