  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.
