Sigma models as perturbed conformal field theories

TL;DR

This paper demonstrates that two-dimensional sigma models can be understood as perturbed conformal field theories, providing new insights and computational methods for models like O(n) and CP^n.

Contribution

It establishes a correspondence between sigma models and perturbed conformal field theories, enabling new analytical approaches and results.

Findings

Derived free energy for O(n) sigma model at non-zero temperature

Linked sigma models to the $k oigackslash ext{infty}$ limit of coset models

Introduced a new approach to the CP^n model

Abstract

We show that two-dimensional sigma models are equivalent 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, the corresponding conformal field theory is the $k\to\infty$ limit of the coset model $(G/H)_k$, and the perturbation is related to the current of G. This correspondence allows us for example to find the free energy for the "O(n)" (=O(n)/O(n-1)) sigma model at non-zero temperature. It also results in a new approach to the CP^{n} model.