Generalised integrable $\lambda$- and $\eta$-deformations and their relation

TL;DR

This paper introduces two-parameter integrable deformations of 2D field theories that connect conformal field theories with non-Abelian T-duals, revealing their relation to bi-Yang-Baxter $\\eta$-deformations and analyzing their quantum properties.

Contribution

The authors construct new two-parameter integrable $\\lambda$-deformations related to bi-Yang-Baxter $\\eta$-deformations, demonstrating their integrability, quantum behavior, and renormalizability.

Findings

Deformations interpolate between WZW models and non-Abelian T-duals.

Deformations are related to bi-Yang-Baxter $\\eta$-deformations via Poisson-Lie T-duality.

Bi-Yang-Baxter $\\sigma$-model is one-loop renormalisable.

Abstract

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.