 In particular, in gauge theory with formula_2 extended supersymmetry, the moduli space of vacua is a special Kähler manifold and its Kähler potential is constrained by above conditions.In the original approach,  by Seiberg and Witten, holomorphy and electric-magnetic duality constraints are strong enough to almost uniquely 
constrain the prepotential, and therefore the metric of the moduli space of vacua, for theories with formula_3 gauge group.More generally, consider the example with gauge group SU(n).