B.R.S. renormalisation of some on-shell closed algebras of symmetry transformations : the example of supersymmetric non-linear sigma models : the N=1 case

TL;DR

This paper uses algebraic BRS methods to rigorously prove the renormalisability of N=1 supersymmetric non-linear sigma models, especially on coset spaces, without relying on regularisation.

Contribution

It provides the first rigorous proof of renormalisability for N=1 supersymmetric non-linear sigma models using algebraic BRS techniques, including models on coset spaces.

Findings

Proved renormalisability of N=1 supersymmetric sigma models.

Extended analysis to models on coset spaces G/H.

Framework applicable to models without off-shell formulations.

Abstract

In order to study in a regularisation free manner the renormalisability of d=2 supersymmetric non-linear $\si$ models, one has to use the algebraic BRS methods ; moreover, in the absence of an off-shell formulation, one has often to deal with open algebras. We then recall in a pedagogical and non technical manner the standard methods used to handle these questions and illustrate them on N=1 supersymmetric non-linear $\si$ model in component fields, giving the first rigorous proof of their renormalisability. In the special case of compact homogeneous manifolds (non-linear $\si$ model on a coset space G/H), we obtain the supersymmetric extension of the analysis done some years ago in the bosonic case. A further publication will be devoted to extended supersymmetry.