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Integrable Deformations of Sigma Models

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arxiv 2109.14284 v3 pith:GBITGCCH submitted 2021-09-29 hep-th math-phmath.MPnlin.SI

Ben Hoare This is my paper
classification hep-thmath-phmath.MPnlin.SI
keywords deformationsintegrablemodelsdualitiesmodelreviewsigmaalgebraic
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Time-Dependent Integrability from Gauge Theory, I

    hep-th 2026-07 accept novelty 7.5 of 10

    Spacetime-dependent 4d Chern-Simons theory generates time-dependent integrable field theories whose allowed time dependence coincides with one-loop RG flow while preserving Lax integrability.

  2. Tree-level S matrix for $\lambda$-deformed AdS3 strings

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    For the λ-deformed AdS3×S3×T4 superstring, the tree-level bosonic worldsheet S matrix is purely elastic for 0≤λ<1, confirming integrability, and ill-defined at λ→1, so that limit does not capture T-dual worldsheet dynamics.

  3. On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model

    hep-th 2026-01 conditional novelty 7.0 of 10

    A new family of commuting local conserved charges in the SU(2) WZNW model is constructed for the first four spins and shown to agree with Bethe-ansatz and ODE/quantum-field-theory predictions.

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