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

A. T. Banin·I. L. Buchbinder·N. G. Pletnev
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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.

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A. T. Banin, I. L. Buchbinder, N. G. Pletnev. 2003-04-14. One-loop effective action for ${\cal N}=4$ SYM theory in the hypermultiplet sector - leading low-energy approximation and beyond. https://doi.org/10.1103/physrevd.68.065024

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