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Non-Abelian conifold transitions and \(N=4\) dualities in three dimensions. (English) Zbl 0934.81049

Summary: 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32G81 Applications of deformations of analytic structures to the sciences
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32S45 Modifications; resolution of singularities (complex-analytic aspects)
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
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