DUALITY AND EXACT RESULTS IN PRODUCT GROUP THEORIES

We study the non-perturbative behavior of some N = 1 supersymmetric pr oduct-group gauge theories with the help of duality, As a test case we investigate an SU(2) x SU(2) theory in detail, Various dual theories are constructed using known simple-group duality for one group or both groups in succession. Several stringent tests show that the low-energ y behavior of the dual theories agrees with that of the electric theor y. When the theory is in the confining phase we calculate the exact su perpotential. Our results strongly suggest that, in general, dual theo ries for product groups can be constructed in this manner, by using si mple-group duality for both groups, Turning to a class of theories wit h SU(N) x SU(M) gauge symmetry we study the renormalization group flow s in the space of the two gauge couplings and show that they are consi stent with the absence of phase transitions. Finally, we show that a s ubset of these theories, with SU(N) x SU(N - 1) symmetry break supersy mmetry dynamically.