Complex structures and zero-curvature equations for sigma-models

TL;DR

This paper develops zero-curvature representations for sigma-models with complex homogeneous target spaces, extending known methods to non-symmetric cases and relating them to traditional models in symmetric scenarios.

Contribution

It introduces a new construction of zero-curvature representations for a broad class of sigma-models with complex target spaces, including non-symmetric cases.

Findings

Zero-curvature representations are constructed for non-symmetric complex homogeneous sigma-models.

In symmetric cases, the new flat connection is gauge-equivalent to the standard one.

The approach generalizes integrability techniques to a wider class of models.

Abstract

We construct zero-curvature representations for the equations of motion of a class of sigma-models with complex homogeneous target spaces, not necessarily symmetric. We show that in the symmetric case the proposed flat connection is gauge-equivalent to the conventional one.