Effective action of N = 4 super Yang-Mills: N = 2 superspace approach

Abstract Using the N =2 off-shell formulation in harmonic superspace for N =4 super Yang–Mills theory, we present a representation of the one-loop effective action which is free of so-called coinciding harmonic singularities and admits a straightforward evaluation of low-energy quantum corrections in the framework of an N =2 superfield heat kernel technique. We illustrate our approach by computing the low-energy effective action on the Coulomb branch of SU(2) N =4 super Yang–Mills. Our work provides the first derivation of the low-energy action of N =4 super Yang–Mills theory directly in N =2 superspace without any reduction to N =1 superfields and for a generic background N =2 Yang–Mills multiplet.