Holomorphic effective action of N=2 SYM theory from harmonic superspace with central charges

We compute the one-loop holomorphic effective action of the massless Cartan sector of N = 2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal compon ents of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N = 2 supersymmetry with the cen tral charges induced by Cartan generators. The (anti)holomorphic part prove s to be proportional to the central charges and it has the generic form of Seiberg's action obtained by integrating U(1)(R) anomaly. It vanishes for N = 4 SYM theory, i.e. the coupled system of N = 2 gauge superfield and hype rmultiplet in the adjoint representation.