N = 1 DUALITIES FOR EXCEPTIONAL GAUGE GROUPS AND QUANTUM GLOBAL SYMMETRIES

We discuss our attempts to generalize the known examples of dualities in N=1 supersymmetric gauge theories to exceptional gauge groups. We d erive some dual pairs from known examples connected to exceptional gro ups and find an interesting phenomenon: sometimes the full global symm etry is ''hidden'' on the magnetic side. It is not realized as a symme try on the fundamental fields in the Lagrangian. Rather, it emerges as a symmetry of the quantum theory. We then focus on an approach based on self-dual models. We construct duals for some very special matter c ontent of E-7, E-6 and F-4. Again we find that the full global symmetr y is not realized on the fundamental fields.