Supersymmetric Euler-Heisenberg effective action: Two-loop results

TL;DR

This paper computes the two-loop supersymmetric Euler-Heisenberg effective action in N=1 supersymmetric QED using background field methods, revealing a closed-form expression for the holomorphic sector under super self-duality.

Contribution

It provides the first two-loop calculation of the effective action in N=1 supersymmetric QED with a general background, extending previous results for N=2 supersymmetry.

Findings

Closed-form expression for the holomorphic sector obtained.

Two-loop renormalisation performed with proper-time cut-off.

Calculation demonstrates increased complexity compared to N=2 case.

Abstract

The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} = const, but is otherwise completely arbitrary. Technically, this calculation proves to be much more laborious as compared with that carried out in hep-th/0308136 for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation. A closed-form expression is obtained for the holomorphic sector of the two-loop effective action, which is singled out by imposing a relaxed super self-duality condition.