Sigma Models as Perturbed Conformal Field Theories

We show that two-dimensional sigma models are related to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, we argue that the corresponding conformal field theory is the k→∞ limit of the coset model (G/H)_k, and the perturbation is related to the current of G. Nonperturbative instanton contributions to the sigma model free energy are perturbative when k is finite. We use this mapping to find the free energy for the “ O(n)” [  = O(n)/O(n-1)] sigma model at nonzero temperature. It also results in a new approach to the CPⁿ model.