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

Abstract

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

LaTeX, 26 pages; corrected typos; references added

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