Dualisation of the principal sigma model

TL;DR

This paper develops a first-order formulation of the principal sigma model with a Lie group target, using dualization and extended symmetry algebra to express field equations through Bianchi identities.

Contribution

It introduces a novel dualization approach and constructs an extended symmetry algebra to represent the model's field equations in a unified framework.

Findings

Derived the structure of the extended symmetry algebra

Expressed field equations as Bianchi identities

Unified formulation of the sigma model's dynamics

Abstract

The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the field strengths are realized through an extended symmetry algebra parametrization. The structure of this symmetry algebra is derived so that it generates the realization of the field equations in a Bianchi identity of the current derived from the extended parametrization.