Integrable interpolations: From exact CFTs to non-Abelian T-duals

TL;DR

Sfetsos develops two classes of integrable two-dimensional theories that interpolate between exact CFTs with affine current algebras $G_k$ and non-Abelian T-duals of the PCM or geometric cosets by gauging a symmetry of the combined WZW/PCM actions. The integrable structure is encoded in current-algebra–type Poisson brackets and a gauging procedure that yields a non-singular background, with explicit SU(2) examples and coset extensions illustrating the interpolation. In the large-level or parafermion-perturbed limits the models reduce to non-Abelian T-duals, while near the CFT point they correspond to perturbed WZW or coset CFTs, tying parafermions to the deformation mechanism. This framework clarifies global properties of non-Abelian T-dual backgrounds and suggests pathways for gravity embeddings and AdS/CFT applications, while highlighting a systematic route to preserve integrability under duality and deformations.

Abstract

We derive two new classes of integrable theories interpolating between exact CFT WZW or gauged WZW models and non-Abelian T-duals of principal chiral models or geometric coset models. They are naturally constructed by gauging symmetries of integrable models. Our analysis implies that non-Abelian T-duality preserves integrability and suggests a novel way to understand the global properties of the corresponding backgrounds.