Integrable deformations of T-dual $\sigma$ models

TL;DR

This paper introduces a method to deform T duals of two-dimensional sigma models that maintains classical integrability, using a linear operator satisfying the 2-cocycle condition, unifying various known deformations.

Contribution

It provides a new framework for integrable deformations of T dual sigma models, connecting homogeneous Yang-Baxter deformations to a broader class of models through a linear operator approach.

Findings

Deformation preserves classical integrability of T dual models.

Homogeneous Yang-Baxter deformations are equivalent to the proposed models when the operator is invertible.

Method applied to Principal Chiral Models and supercoset models.

Abstract

We present a method to deform (generically non-abelian) T duals of two-dimensional $\sigma$ models, which preserves classical integrability. The deformed models are identified by a linear operator $\omega$ on the dualised subalgebra, which satisfies the 2-cocycle condition. We prove that the so-called homogeneous Yang-Baxter deformations are equivalent, via a field redefinition, to our deformed models when $\omega$ is invertible. We explain the details for deformations of T duals of Principal Chiral Models, and present the corresponding generalisation to the case of supercoset models.