Integrable sigma models and perturbed coset models

TL;DR

This paper computes the exact free energy for two classes of integrable sigma models in two dimensions, revealing their thermodynamic properties and conformal limits, with implications for particle and condensed matter physics.

Contribution

It provides the first exact free energy calculations for the SU(N)/SO(N) and O(2P)/O(P) x O(P) integrable sigma models, including their perturbed conformal field theories.

Findings

Exact free energy at any temperature for the models.

Demonstration of flow to conformal field theories at theta=pi.

Extension to massive and massless perturbations of coset CFTs.

Abstract

Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two dimensions. These theories, the SU(N)/SO(N) and O(2P)/O(P) x O(P) models, are asymptotically free and exhibit charge fractionalization. When the instanton coupling theta=pi, they flow to the SU(N)_1 and O(2P)_1 conformal field theories, respectively. I also generalize the free energy computation to massive and massless perturbations of the coset conformal field theories SU(N)_k/SO(N)_{2k} and O(2P)_k/O(P)_k x O(P)_k.