Hypermultiplet effective action: N=2 superspace approach

In an earlier Letter (hep-th/0101127), we developed heat kernel techniques in N=2 harmonic superspace for the calculation of the low-energy effective action of N=4 SYM theory, which can be considered as the most symmetric N=2 SYM theory. Here, the results are extended to generic N=2 SYM theories. This involves a prescription for computing the variation of the hypermultiplet effective action. Integrability of this variation allows the hypermultiplet effective action to be deduced. This prescription permits a very simple superfield derivation of the perturbative holomorphic prepotential. Explicit calculations of the prepotential and the leading non-holomorphic correction are presented.