Integrability vs. RG flow in G × G and G × G/H sigma models

Abstract

Abstract We consider a class of 2d σ-models on products of group spaces that provide new examples of a close connection between integrability and stability under the RG flow. We first study the integrable G × G model derived from the affine Gaudin construction (for which the 1-loop β-functions were found in arXiv:2010.07879 ) and show that its condition of integrability is preserved also by the 2-loop RG flow. We then investigate the RG flow in the gauged G × G/H model, in particular the integrable T 1,1 model found in arXiv:2010.05573 . We also construct a new class of integrable G × G/H models in the case when the subgroup H is abelian. In the simplest case of G = SU 2 , H = U 1 this leads to an integrable σ-model on the T 1,q space (with a particular B-field). This model is also shown to be stable under the 2-loop RG flow, and we relate this property to its invariance under T-duality in an isometric U 1 direction. This T 1,q model may be interpreted as an integrable deformation of the GMM model (of two coupled WZW theories with generic levels) away from the conformal point.

Keywords

• Integrable Field Theories
• Renormalization Group
• Sigma Models