Low-energy dynamics in N = 2 super QED : two-loop approximation

The two-loop (Euler-Heisenberg-type) effective action for N = 2 supersymmetric QED is computed using the N = 1 superspace formulation. The effective action is expressed as a series in supersymmetric extensions of F2n, where n = 2,3,..., with F the field strength. The corresponding coefficients are given by triple proper-time integrals which are evaluated exactly. As a by-product, we demonstrate the appearance of a non-vanishing F4 quantum correction at the two-loop order. The latter result is in conflict with the conclusion of [1] that no such quantum corrections are generated at two loops in generic N = 2 SYM theories on the Coulomb branch. We explain a subtle loophole in the relevant consideration of [1] and re-derive the F4 term from harmonic supergraphs.