One-loop effective action for N=4 SYM theory in the hypermultiplet sector:: Leading low-energy approximation and beyond -: art. no. 065024

We develop the derivative expansion of the one-loop N=4 super Yang-Mills (SYM) effective action depending both on the N=2 vector multiplet and on hypermultiplet background fields. Beginning with the formulation of N=4 SYM theory in terms of N=1 superfields, we construct the one-loop effective action with the help of superfield functional determinants and calculate this effective action in N=1 superfield form using the approximation of constant Abelian strength F-mn and corresponding constant hypermultiplet fields. Then we show that the terms in the supercovariant derivative expansion of the effective action can be rewritten in terms of N=2 superfields. As a result, we get a new derivation of the complete N=4 supersymmetric low-energy effective action obtained by Buchbinder and Ivanov and find subleading corrections to it.