Non-Abelian conifold transitions and N=4 dualities in three dimensions

We show how the Higgs mechanism for non-Abelian N=2 gauge theories in 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 circle to derive N=4, d=3 dual field theories. This reduces the dualities for N=4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover, we find that the dual of a gauge system always exists but may or may not correspond to a Lagrangian system. In particular, we verify a conjecture of Intriligator and Seiberg that an ordinary gauge system is dual to compactification of exceptional tensionless string theory down to three dimensions. (orig.)