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Effective Action in ${\cal N}=2,4$ Supersymmetric Yang-Mills Theories

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

We review the approach to calculation of one-loop effective action in ${\cal N}=2,4$ SYM theories. We compute the non-holomorphic corrections to low-energy effective action (higher derivative terms) in ${\cal N}=2$, SU(2) SYM theory coupled to hypermultiplets on a non-abelian background for $R_ξ$-gauge fixing conditions. A general procedure for calculating the gauge parameters depending contributions to one-loop superfield effective action is developed. The one-loop non-holomorphic effective potential is exactly found in terms of the Euler dilogarithm function for a specific choice of gauge parameters.We also discuss the calculations of hypermultiplet dependence of ${\cal N}=4$ SYM effective action.

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A. T. Banin, I. L. Buchbinder, N. G. Pletnev. 2003-09-08. Effective Action in ${\cal N}=2,4$ Supersymmetric Yang-Mills Theories. https://arxiv.org/abs/hep-th/0309048

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