Supersymmetric Euler-Heisenberg effective action: Two-loop results

Abstract

The two-loop Euler-Heisenberg-type effective action for ≤ 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D αWβ ≤ D(αW β) ≤ 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 ≤ 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis of 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. © SISSA 2007.