Computation of the central charge for the leading order of the N=2 super-Yang-Mills effective action

The central charge in the N = 2 super-Yang-Mills theory plays an essential role in the work of Seiberg and Witten as it gives the mass spectrum of the BPS states of the quantum theory. Our aim in this letter is to present a direct computation of this central charge for the leading order (in a momentum expansion) of the effective action. We will consider the N = 2 super-Yang-Mills theory with gauge group SU(2). The leading order of the effective action is given by the same holomorphic function F appearing in the low energy U(1) effective action.