Integrable Deformations of Sigma Models

TL;DR

This review systematically explores deformations of integrable 2D sigma models, focusing on Yang-Baxter and current-current deformations, their algebraic structures, and applications to string theory, including original results on Z T cosets.

Contribution

It provides a comprehensive pedagogical overview of integrable deformations of sigma models, introducing new results on Z T cosets and their relevance to string theory.

Findings

Relations between models based on algebraic structures and dualities

Development of deformation techniques for principal chiral and WZW models

Application of deformations to string theory contexts

Abstract

In this pedagogical review we introduce systematic approaches to deforming integrable 2-dimensional sigma models. We use the integrable principal chiral model and the conformal Wess-Zumino-Witten model as our starting points and explore their Yang-Baxter and current-current deformations. There is an intricate web of relations between these models based on underlying algebraic structures and worldsheet dualities, which is highlighted throughout. We finish with a discussion of the generalisation to other symmetric integrable models, including some original results related to Z T cosets and their deformations, and the application to string theory. This review is based on notes written for lectures delivered at the school "Integrability, Dualities and Deformations", which ran from 23 to 27 August 2021 in Santiago de Compostela and virtually.