Nonlinearσmodel as a local polynomial field theory

The nonlinear $\sigma$ model is reformulated as a field theory that does not involve nonpolynomial interactions. This reformulation introduces an antisymmetric tensor field in the theory and associated gauge symmetries. After the introduction of a regularizing term and gauge fixing, we obtain a perturbation theory that is renormalizable by power counting. The regularizing term causes the perturbation theory to lose unitarity at a scale that can be adjusted by the coefficient of this term.