Generalised integrable λ- and η-deformations and their relation

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 SU(2) WZW model and the SU(2)/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. (C) 2015 The Authors. Published by Elsevier B.V.