Symmetries in a Polynomial Formulation of the Non-Linear Sigma-Model

TL;DR

This paper explores how global symmetries are represented in a polynomial formulation of the non-linear sigma-model, revealing that some symmetries correspond to topological currents and others become non-local.

Contribution

It demonstrates the realization of global symmetries as topological currents and analyzes the locality properties of Noether currents in the polynomial formulation.

Findings

Topological currents correspond to certain global symmetries.

Some Noether currents become non-local in the polynomial formulation.

The polynomial formulation reproduces internal symmetry currents.

Abstract

We study the realisation of global symmetries in a polynomial formulation of the non-linear sigma-model. We show that there are global symmetries whose corresponding Noether currents are the topological currents in the usual formulation. The usual Noether currents associated with the internal symmetry group are reproduced, but part of them become non-local in terms of the dynamical variables of the polynomial formulation.