Perturbation theory in supersymmetric QED: Infrared divergences and gauge invariance

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 one particle irreducible (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.

Figure 1

One-loop contribution to the helicity-flip process.

Figure 2

One-loop contributions to the helicity-preserving process.

Figure 3

Diagrams contributing to the ${\mathrm{\Phi }}_0$ effective Lagrangian at two loops.

Figure 4

Correction to the $⟨aa⟩$ two-point function.