Relaxed super self-duality and effective action

TL;DR

This paper derives a closed-form expression for a specific holomorphic sector of the two-loop effective action in N=2 supersymmetric QED, using a relaxed super self-duality condition, with implications for N=4 super Yang-Mills theory.

Contribution

It introduces a novel approach to compute a holomorphic sector of the two-loop effective action in supersymmetric theories using relaxed super self-duality.

Findings

Derived a closed-form expression for the holomorphic sector of the two-loop effective action.

Applied the method to N=2 supersymmetric QED and discussed potential extensions to N=4 super Yang-Mills.

Provided a new technique for analyzing effective actions in supersymmetric gauge theories.

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.