Integrable theories in any dimension and homogenous spaces

TL;DR

This paper develops a method to construct local zero curvature representations for non-linear sigma models on homogeneous spaces across any dimension, identifying conditions for integrability and providing examples including $CP^N$ models.

Contribution

It introduces a new approach to higher-dimensional integrable theories by constructing zero curvature representations for sigma models on homogeneous spaces.

Findings

Established sufficient conditions for integrable submodels with infinite conservation laws.

Provided explicit examples involving symmetric spaces and group manifolds.

Detailed analysis of $CP^N$ models in the context of integrability.

Abstract

We construct local zero curvature representations for non-linear sigma models on homogeneous spaces, defined on a space-time of any dimension, following a recently proposed approach to integrable theories in dimensions higher than two. We present some sufficient conditions for the existence of integrable submodels possessing an infinite number of local conservation laws. Examples involving symmetric spaces and group manifolds are given. The $CP^N$ models are discussed in detail.