Infinite Family of Integrable Sigma Models Using Auxiliary Fields

TL;DR

This paper introduces a broad class of two-dimensional sigma models with auxiliary fields, proving their classical integrability and including known models like the principal chiral model and its deformations.

Contribution

The authors define a new family of integrable sigma models parameterized by a function, extending known models and establishing their classical integrability via Lax pairs.

Findings

All models in the family are classically integrable.

The models include the principal chiral model and its energy-momentum tensor deformations.

An explicit Lax representation is constructed for these models.

Abstract

We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_\alpha$ which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.