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Construction of one-loop ${\cal N}=4$ SYM effective action on the mixed branch in the harmonic superspace approach

I. L. Buchbinder·N. G. Pletnev
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Abstract

We develop a systematic approach to construct the one-loop ${\cal N}=4$ SYM effective action depending on both ${\cal N}=2$ vector multiplet and hypermultiplet background fields. Beginning with the formulation of ${\cal N}=4$ SYM theory in terms of ${\cal N}=2$ harmonic superfields, we construct the one-loop effective action using the covariant ${\cal N}=2$ harmonic supergraphs and calculate it in ${\cal N}=2$ harmonic superfield form for constant Abelian strength $F_{mn}$ and corresponding constant hypermultiplet fields. The hypermultiplet-dependent effective action is derived and given by integral over the analytic subspace of harmonic superspace. We show that each term in the Schwinger-De Witt expansion of the low-energy effective action is written as integral over full ${\cal N}=2$ superspace.

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I. L. Buchbinder, N. G. Pletnev. 2005-07-18. Construction of one-loop ${\cal N}=4$ SYM effective action on the mixed branch in the harmonic superspace approach. https://doi.org/10.1088/1126-6708%2F2005%2F09%2F073

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