MIRROR SYMMETRY IN 3-DIMENSIONAL GAUGE-THEORIES, QUIVERS AND D-BRANES

We construct and analyze dual N = 4 supersymmetric gauge theories in t hree dimensions with unitary and symplectic gauge groups. The gauge gr oups and the field content of the theories are encoded in quiver diagr ams. The duality exchanges the Coulomb and Higgs branches and the Faye t-Iliopoulos and mass parameters. We analyze the classical and the qua ntum moduli spaces of the theories and construct an explicit mirror ma p between the mass parameters and the Fayet-Iliopoulos parameters of t he dual. The results generalize the relation between ALE spaces and mo duli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-du ality and extremal transitions in type II string compactifications, fo r SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter. (C) 1997 Elsevier Science B.V.