NON-ABELIAN CONIFOLD TRANSITIONS AND N=4 DUALITIES IN 3 DIMENSIONS

We show how the Higgs mechanism for non-Abelian N = 2 gauge theories i n four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau 3-folds. We use this result and T-duality of a further compactification on a ci rcle to derive N = 4, d = 3 dual field theories. This reduces the dual ities for N = 4 gauge systems in three dimensions to perturbative symm etries of string theory. Moreover, we find that the dual of a gauge sy stem always exists but may or may not correspond to a Lagrangian syste m. In particular, we verify a conjecture of Intriligator and Seiberg t hat an ordinary gauge system is dual to compactification of exceptiona l tensionless string theory down to three dimensions. (C) 1997 Elsevie r Science B.V.