Duality and exact results in product group theories

We study the non-perturbative behavior of some N = 1 supersymmetric product-group gauge theories with the help of duality. As a test case we investigate an SU(2) × 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-energy behavior of the dual theories agrees with that of the electric theory. When the theory is in the confining phase we calculate the exact superpotential. Our results strongly suggest that, in general, dual theories for product groups can be constructed in this manner, by using simple-group duality for both groups. Turning to a class of theories with SU(N) × SU(M) gauge symmetry we study the renormalization group flows in the space of the two gauge couplings and show that they are consistent with the absence of phase transitions. Finally, we show that a subset of these theories, with SU(N) × SU(N - 1) symmetry break supersymmetry dynamically