Integrable sigma models and perturbed coset models

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.