Integrable deformations with twisted quantum affine symmetry

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The study of integrable deformations of 2-d QFTs has led to significant insights into how integrability can be used to find exact, non-perturbative, solutions of quantum theories. Work on Yang-Baxter deformations has been a major part of this remarkable progress, resulting in the potential discovery of new integrable string sigma models and holographic dualities. Yang-Baxter deformations fall into two classes: twists and q-deformations; however, many of the q-deformed models have intractable features, such as a singular target space geometry. In this project the student will investigate generalisations of q-deformed models, which are expected to have twisted quantum affine symmetry. Having constructed the deformed sigma models, the student will investigate the Lie-Poisson structure to derive and confirm their symmetries. Following on from this, the deformations will be generalised to Z2 and Z4 cosets, with the goal of constructing new, more tractable, integrable deformations of string sigma models on AdS backgrounds.