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 derive some dual pairs from known examples connected to exceptional groups and find an interesting phenomenon: sometimes the full global symmetry is “hidden” on the magnetic side. It is not realized as a symmetry 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 content of E7, E6 and F4. Again we find that the full global symmetry is not realized on the fundamental fields. ∗Work supported in part by NSF Grant PHY9511632, the Robert A. Welch Foundation, an Alfred P. Sloan Foundation Fellowship and the DAAD.