Duality And Braids In N=2 Yang-Mills Theories

We briefly report the general form of the electromagnetic duality group \Gamma D for an arbitrary N = 2 rigidly supersymmetric SU(r+1) gauge theory, which extends previous explicit constructions for the r = 1; 2 cases. The results are obtained by a method that had proven useful in the past to study Calabi-Yau moduli spaces for more than one parameter, and exploits the relation between monodromy and braid groups for algebraic surfaces . A better grasp on nonperturbative aspects of supersymmetric gauge theories has been reached after the observation that the quantum moduli space for the abelian phase of a G invariant N = 2 rigid gauge theory can be characterized in terms of a class of genus r = rank G hyperelliptic Riemann surfaces \Sigma r , parametrized by r complex moduli, and informations on the electromagnetic duality symmetries of the theory can be extracted from the monodromy group of \Sigma r 1\Gamma3 . More precisely, the electromagnetic duality group \Gamma D can be inferre..