RG flows of integrable $\sigma$-models and the twist function

TL;DR

This paper demonstrates that for a broad class of integrable non-linear sigma models, the renormalization group flow can be succinctly expressed using the twist function, revealing a universal structure in their behavior.

Contribution

It establishes the one-loop renormalizability of these models and derives a simple, universal RG flow equation directly in terms of the twist function.

Findings

Models are one-loop renormalizable.

RG flow equations are expressed via the twist function.

Universal RG flow structure identified.

Abstract

In the study of integrable non-linear $\sigma$-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central role. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.