SOME EXACT RESULTS IN SUPERSYMMETRIC THEORIES BASED ON EXCEPTIONAL GROUPS

We begin an investigation of supersymmetric theories based on exceptio nal groups. The hat directions are most easily parametrized using thei r correspondence with gauge-invariant polynomials. Symmetries and holo morphy tightly constrain the superpotentials, but due to multiple gaug e invariants other techniques are needed for their full determination. We give an explicit treatment of G(2) and find gaugino condensation f or N-f less than or equal to 2, and an instanton generated superpotent ial for N-f = 3. The analogy with SU(N-c) gauge theories continues wit h modified and unmodified quantum moduli spaces for N-f = 4 and N-f = 5, respectively, and a non-Abelian Coulomb phase for N-f greater than or equal to 6. Electric variables suffice to describe this phase over the full range of N-f. The Appendix gives a self-contained introductio n to G(2) and its invariant tensors.