Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies

TL;DR

This paper develops a supersymmetry-preserving Wilson renormalization group framework for supersymmetric gauge theories, deriving flow equations, addressing gauge symmetry restoration, and reproducing the supersymmetric chiral anomaly at one loop.

Contribution

It introduces a supersymmetry-preserving RG scheme applicable to supersymmetric gauge theories, including derivation of flow equations and anomaly reproduction.

Findings

RG flow for the massless Wess-Zumino model derived

Gauge symmetry can be restored via boundary conditions in the RG flow

Reproduces the one-loop supersymmetric chiral anomaly to second order

Abstract

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization- can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.