One-loop effective action for ${\cal N}=4$ SYM theory in the hypermultiplet sector - leading low-energy approximation and beyond

TL;DR

This paper develops a derivative expansion method to derive the complete low-energy effective action of ${ m extbf{N}=4}$ SYM theory, including subleading corrections, using ${ m extbf{N}=2}$ harmonic superspace and exploring hidden supersymmetry.

Contribution

It introduces a new derivation of the ${ m extbf{N}=4}$ supersymmetric effective action and identifies subleading corrections using harmonic superspace formalism.

Findings

Derived the complete ${ m extbf{N}=4}$ supersymmetric low-energy effective action.

Identified subleading corrections to the effective action.

Constructed the ${ m extbf{N}=4}$ supersymmetric functional containing $F^{8}$.

Abstract

We develop the derivative expansion of the one-loop ${\cal N}=4$ SYM effective action depending both on ${\cal N}=2$ vector multiplet and on hypermultiplet background fields. We get a new derivation of the complete ${\cal N}=4$ supersymmetric low-energy effective action obtained in hep-th/0111062 and find subleading corrections to it. A problem of ${\cal N}=4$ supersymmetry of the results is discussed. Using the formalism of ${\cal N}=2$ harmonic superspace and exploring on-shell hidden ${\cal N}=2$ supersymmetry of ${\cal N}=4$ SYM theory we construct the appropriate hypermultiplet-depending contributions. The hidden ${\cal N}=2$ supersymmetry requirements allow to get a leading, in hypermultiplet derivatives, part of the correct ${\cal N}=4$ supersymmetric functional containing $F^{8}$ among the component fields.