RG Flow Irreversibility , C - Theorem and Topological Nature of 4 D N = 2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N = 2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg–Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non–perturbative identity relating the u–modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c–theorem for N = 2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.