Renormalization and Symmetry Conditions in Supersymmetric QED

TL;DR

This paper develops a method within algebraic renormalization to maintain supersymmetry and gauge invariance in supersymmetric QED, providing practical tools for calculating counterterms and analyzing symmetry restoration at one-loop order.

Contribution

It introduces symmetry conditions derived from the Slavnov--Taylor identity that relate physical quantities and facilitate counterterm determination in supersymmetric QED.

Findings

Derived symmetry conditions valid to all orders

Demonstrated counterterm calculation in dimensional regularization

Showed modifications of supersymmetry transformations at one-loop

Abstract

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov--Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms.