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) models and the O(2P)/O(P) × O(P) models, are asymptotically free and exhibit charge fractionalization. When the instanton coupling 9 = TT, 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 conformai field theories SU(N)k/ SO(N)2k and O(2P)k/O(P)k × O(P)k.