The geometric background-field method, renormalization and the Wess-Zumino term in non-linear σ-models

Abstract

A simple recursive algorithm is presented which generates the reparametrization-invariant background-field expasion for non-linear σ-models on manifolds with an arbitrary riemannian metric. The method is also applicable to Wess-Zumino terms and to counterterms. As an example, the general-metric model is expanded to sixth order and compared with previous results. For locally symmetric spaces, we actually obtain a general formula for the nth order term. The method is shown to facilitate the study of models with Wess-Zumino terms. It is demonstrated that, for chiral models, the Wess-Zumino term is unrenormalized to all orders in perturbation theory even when the model is not conformally invariant.