Central charge as the origin of holomorphic effective action in N=2 gauge theory

We show explicitly that the perturbative holomorphic contribution to the off-shell effective action of N=2 U(1) gauge supermultiplet is an entire effect of the minimal coupling to a hypermultiplet with the mass generated by a central charge in N = 2 superalgebra. The central charge is induced by a constant vacuum N = 2 gauge superfield strength spontaneously breaking the automorphism U(1)R symmetry of N = 2 superalgebra. We use the manifestly off-shell supersymmetric harmonic superspace techniques of quantum calculations with the central charge-massive hypermultiplet propagator.