Renormalization of non-linear sigma models: A short review

Abstract

We shall sketch the renormalization procedure for non-linear σ-models built on compact, homogeneous coset spaces; the analysis is based on the construction of a nilpotent B.R.S. operator which controls the ultraviolet counterterms and also allows the proof of the existence of the zero-mass limit for the observables of these models. The attention will be focused on the methodology and results; references are given for the technical aspects. The extension to compact Riemannian manifolds and the supersymmetric cases are briefly touched upon in the conclusions.