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Generalised integrable \(\lambda\)- and \(\eta\)-deformations and their relation. (English) Zbl 1331.81248
Summary: We construct two-parameter families of integrable \(\lambda\)-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the \(\operatorname{SU}(2)\) WZW model and the \(\operatorname{SU}(2) / \operatorname{U}(1)\) exact coset CFT, we show that these deformations are related to bi-Yang-Baxter generalisations of \(\eta\)-deformations via Poisson-Lie T-duality and analytic continuation. We illustrate the quantum behaviour of our models under RG flow. As a byproduct we demonstrate that the bi-Yang-Baxter \(\sigma\)-model for a general group is one-loop renormalisable.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
14D15 Formal methods and deformations in algebraic geometry
81T17 Renormalization group methods applied to problems in quantum field theory
81T18 Feynman diagrams
16T25 Yang-Baxter equations
22E70 Applications of Lie groups to the sciences; explicit representations
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