Flag manifold sigma-models and nilpotent orbits

TL;DR

This paper explores flag manifold sigma-models with zero-curvature representation, linking them to holomorphic and anti-holomorphic beta-gamma systems and establishing a connection to the principal chiral model via nilpotent orbits.

Contribution

It introduces a novel perspective on flag manifold sigma-models as interacting beta-gamma systems and relates them to the principal chiral model through nilpotent orbit theory.

Findings

Flag manifold sigma-models admit a zero-curvature representation.

Models can be viewed as interacting holomorphic and anti-holomorphic beta-gamma systems.

Established a relation between these models and the principal chiral model using nilpotent orbits.

Abstract

In the present paper we study flag manifold sigma-models that admit a zero-curvature representation. It is shown that these models may be naturally considered as interacting (holomorphic and anti-holomorphic) $\beta\gamma$-systems. Besides, using the theory of nilpotent orbits of complex Lie groups, we establish a relation to the principal chiral model.