Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

TL;DR

This paper demonstrates that supersymmetric gauge theories with dimensionful parameters do not have perturbative soft anomalies, using algebraic renormalization and spurion analysis to extend previous anomaly results.

Contribution

It provides a rigorous proof that soft anomalies are absent in such theories, filling gaps in earlier incomplete arguments.

Findings

No perturbative soft anomalies found in supersymmetric gauge theories with dimensionful parameters.

The combination of algebraic renormalization and spurion analysis effectively rules out quantum violations of supersymmetry.

The method works in the on-shell formalism with dynamical spurions, which can be decoupled.

Abstract

It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of Algebraic Renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.