Algebraic renormalization of N=2 Super Yang-Mills theories coupled to matter

TL;DR

This paper uses algebraic renormalization to analyze N=2 Super Yang-Mills theories coupled to matter, demonstrating the absence of anomalies and the quantum correction of the sole coupling constant.

Contribution

It provides a regularization-independent algebraic proof that N=2 SYM coupled to matter is free of anomalies and identifies the quantum correction of the coupling constant.

Findings

The theory's symmetries are algebraically anomaly-free.

The only coupling constant receives quantum corrections.

A regularization scheme preserving all symmetries is not yet known.

Abstract

We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, therefore it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides to unphysical renormalizations of the quantum fields, we find that the only coupling constant of $N=2$ SYMs can get quantum corrections. Moreover we prove that all the symmetries defining the theory are algebraically anomaly--free.