RG flow of integrable E-models

Abstract

We compute the one- and two-loop RG flow of integrable σ-models with Poisson-Lie symmetry. They are characterised by a twist function with 2N simple poles/zeros and a double pole at infinity. Hence, they capture many of the known integrable deformations in a unified framework, which has a geometric interpretation in terms of surface defects in a 4D Chern-Simons theory. We find that these models are one-loop renormalisable and present a very simple expression for the flow of the twist function. At two loops only models with N=1 are renormalisable. Applied to the λ-deformation on a semisimple group manifold, our results reproduce the β-functions in the literature.