Integrable Deformations of Sigma Models

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.

v3: 68 pages, minor comments and references added, matches published version

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Cited by in corpus (15)

• On the Classical Integrability of Root-$T\overline{T}$ Flows
• 4-dimensional Chern-Simons theory and integrable field theories
• Introduction to classical and quantum integrability
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Coset space actions for nonrelativistic strings
• Universal 1-loop divergences for integrable sigma models
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Deformed WZW Models and Hodge Theory -- Part I
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Novel aspects of integrability for NLSMs in symmetric spaces
• Beyond Noether: A Covariant Study of Poisson-Lie Symmetries in Low Dimensional Field Theory
• On the classical Integrability of Poisson-Lie T-dual WZW models