Algebraic Renormalization of $N=1$ Supersymmetric Gauge Theories

TL;DR

This paper develops an algebraic renormalization framework for N=1 supersymmetric gauge theories, ensuring gauge invariance and supersymmetry are preserved during renormalization without regulators.

Contribution

It introduces a unified BRS invariance approach that incorporates gauge invariance and supersymmetry, and clarifies the algebraic structure of anomalies and supersymmetry operators.

Findings

The renormalization procedure preserves supersymmetry and gauge invariance.

The form of the nonabelian anomaly is explicitly given.

Supersymmetry operators form a closed superalgebra on gauge-invariant operators.

Abstract

The complete renormalization procedure of a general N=1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free ``algebraic renormalization'' procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general nonabelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is restricted to the space of the ``gauge invariant operators'', i.e. to the cohomology classes of the gauge BRS operator. An erratum is added at the end of the paper.