Integrable properties of sigma-models with non-symmetric target spaces

TL;DR

This paper investigates the integrability of sigma-models with non-symmetric target spaces, demonstrating that adding torsion to a specific model enables a zero-curvature formulation, suggesting potential integrability.

Contribution

It introduces a method to achieve integrability in non-symmetric sigma-models by incorporating torsion, extending known results from symmetric spaces.

Findings

Torsion enables zero-curvature formulation of equations of motion.

The model with target space U(3)/U(1)^3 exhibits signs of integrability.

Geometric analysis of the proposed model is elaborated.

Abstract

It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition for a one-parametric family of connections, which can be a sign of integrability of the theory. We also elaborate on geometric aspects of the proposed model.