Shadow Fields and Local Supersymmetric Gauges

TL;DR

The paper addresses the challenge of maintaining both supersymmetry and gauge invariance in quantized super-Yang-Mills theories. It introduces shadow fields to extend the Faddeev-Popov framework and to derive a network of Slavnov-Taylor identities that govern both the BRST and supersymmetry structures. Through a detailed cohomological analysis, it classifies possible anomalies, proves the absence of supersymmetry anomalies for N=2 and N=4 (with precise caveats for N=1), and shows that renormalization can be performed in a fully regularization-independent way within a family of interpolating gauges. The approach provides a robust, local, and practical framework for preserving SUSY covariance and gauge invariance in supersymmetric gauge theories, including explicit off-shell examples and gauge families that interpolate between manifestly supersymmetric and conventional Faddeev-Popov fixings.

Abstract

To control supersymmetry and gauge invariance in super-Yang-Mills theories we introduce new fields, called shadow fields, which enable us to enlarge the conventional Faddeev-Popov framework and write down a set of useful Slavnov-Taylor identities. These identities allow us to address and answer the issue of the supersymmetric Yang-Mills anomalies, and to perform the conventional renormalization programme in a fully regularization-independent way.