Relaxed super self-duality and effective action

Abstract A closed-form expression is obtained for a holomorphic sector of the two-loop Euler–Heisenberg type effective action for N =2 supersymmetric QED derived in hep-th/0308136 . In the framework of the background-field method, this sector is singled out by computing the effective action for a background N =2 vector multiplet satisfying a relaxed super self-duality condition. The approach advocated in this Letter can be applied, in particular, to the study of the N =4 super-Yang–Mills theory on its Coulomb branch.