Symmetries in a polynomial formulation of the non-linear σ-model

Abstract We study the realisation of global symmetries in a polynomial (or “linearized”) formulation of the non-linear σ-model. We show that there are global symmetries whose corresponding Noether currents are the topological currents in the usual formulation. The usual (Noether) conserved 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.