Integrability and Diffeomorphisms on Target Space

TL;DR

This paper explores the relationship between integrability, conservation laws, and volume-preserving diffeomorphisms in higher-dimensional field theories, providing a classification for three-dimensional target spaces and discussing explicit examples.

Contribution

It introduces a classification of conservation laws generated by geometric target space transformations in higher-dimensional integrable field theories.

Findings

Conservation laws are generated by volume-preserving diffeomorphisms.

Classified possible conservation laws for three-dimensional target spaces.

Presented explicit examples illustrating the concepts.

Abstract

We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples.