Generalized integrability conditions and target space geometry

TL;DR

This paper explores how generalized integrability conditions in higher-dimensional nonlinear field theories can be derived from the geometry of the target space, linking conservation laws to target space transformations.

Contribution

It introduces a geometric framework connecting integrability conditions to target space geometry and Noether currents, extending previous approaches.

Findings

New integrability conditions derived from target space geometry

Connection established between conservation laws and target space transformations

Framework applicable to higher-dimensional nonlinear field theories

Abstract

In some higher dimensional nonlinear field theories integrable subsectors with infinitely many conservation laws have been identified by imposing additional integrability conditions. Originally, the complex eikonal equation was chosen as integrability condition, but recently further generalizations have been proposed. Here we show how these new integrability conditions may be derived from the geometry of the target space and, more precisely, from the Noether currents related to a certain class of target space transformations.