Effective action of N = 4 super Yang-Mills: N = 2 superspace approach

TL;DR

This paper develops an N=2 superspace method to compute the one-loop effective action of N=4 super Yang-Mills theory, enabling straightforward low-energy quantum correction calculations without reducing to N=1 superspace.

Contribution

It introduces a novel harmonic superspace approach that avoids singularities and allows direct N=2 superspace derivation of the low-energy effective action for N=4 super Yang-Mills.

Findings

First derivation of N=4 super Yang-Mills low-energy action in N=2 superspace.

Effective action representation free of harmonic singularities.

Explicit computation of low-energy corrections on the Coulomb branch.

Abstract

Using the N = 2 off-shell formulation in harmonic superspace for N = 4 super Yang-Mills theory, we present a representation of the one-loop effective action which is free of so-called coinciding harmonic singularities and admits a straightforward evaluation of low-energy quantum corrections in the framework of an N = 2 superfield heat kernel technique. We illustrate our approach by computing the low-energy effective action on the Coulomb branch of SU(2) N = 4 super Yang-Mills. Our work provides the first derivation of the low-energy action of N = 4 super Yang-Mills theory directly in N = 2 superspace without any reduction to N = 1 superfields and for a generic background N = 2 Yang-Mills multiplet.