Comments on the Background Field Method in Harmonic Superspace: Non-holomorphic Corrections in N=4 SYM

TL;DR

This paper investigates the one-loop effective action of N=4 SYM in harmonic superspace, demonstrating its singularity-free nature and computing key non-holomorphic corrections, thus advancing understanding of quantum effects in supersymmetric gauge theories.

Contribution

It provides a detailed analysis of the effective action in harmonic superspace and computes the leading non-holomorphic corrections for N=4 SYM.

Findings

Effective action is free of harmonic singularities for on-shell backgrounds.

Effective action coincides with N=1 background field results when certain components are off.

Computed the leading non-holomorphic corrections to the N=4 SU(2) SYM effective action.

Abstract

We analyse the one-loop effective action of N=4 SYM theory in the framework of the background field formalism in N=2 harmonic superspace. For the case of on-shell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with that obtained by Grisaru et al on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU(2) SYM effective action.