Abstract
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 threefolds. We use this result and T-duality of a further compacitification on a circle to derive N = 4, d = 3 dual field theories. This reduces 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 compacitification of exceptional tensionless string theory down to three dimensions.
HUTP-97/A024, LBNL-40349, UCB-PTH-97/27 hep-th/9705220
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Hori, K., Ooguri, H., Vafa, C. (1998). Non-Abelian Conifold Transitions and N = 4 Dualities in Three Dimensions. In: Kashiwara, M., Matsuo, A., Saito, K., Satake, I. (eds) Topological Field Theory, Primitive Forms and Related Topics. Progress in Mathematics, vol 160. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0705-4_7
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