On the structure of non-commutative N=2 Super Yang-Mills theory

We show that the recently proposed formulation of non-commutative N = 2 Super Yang-Mills theory implies that the commutative and non-commutative effective coupling constants tau (u) and tau (nc)(u) coincide. We then introduce a key relation which allows to find a non-trivial solution of such equation, thus fixing the form of the low-energy effective action. The dependence on the non-commutative parameter arises from a rational function deforming the Seiberg-Witten differential.