Classical Integrability of Two Dimensional Non Linear Sigma Models

TL;DR

This paper establishes conditions for classical integrability in two-dimensional non-linear sigma models by expressing their equations of motion as a zero curvature condition, and introduces new integrable models.

Contribution

It provides a systematic criterion for classical integrability and presents new examples of integrable two-dimensional sigma models.

Findings

Derived conditions for classical integrability

Expressed equations of motion as zero curvature relations

Presented new integrable sigma models

Abstract

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature relation. Some new integrable two-dimensional sigma models are then presented.