Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance

TL;DR

This paper investigates infrared divergences and gauge invariance in perturbation theory of supersymmetric QED, revealing their gauge dependence and the conditions under which they cancel or are avoided, thus clarifying the structure of quantum corrections.

Contribution

It demonstrates how IR divergences in supersymmetric QED cancel in physical quantities and shows the reorganization of perturbation series from powers of e^2 to e, providing new insights into gauge invariance.

Findings

IR divergences are gauge-dependent and cancel in physical observables.

Cancellation involves a reorganization of the perturbation series.

Wilsonian effective actions avoid these IR complications.

Abstract

We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.