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A Geometric Unification of Dualities

F. Cachazo·B. Fiol·K. Intriligator·S. Katz·C. Vafa
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Abstract

We study the dynamics of a large class of N=1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds. These include N=2 (affine) A-D-E quiver theories deformed by superpotential terms, as well as chiral N=1 quiver theories obtained in the presence of vanishing 4-cycles inside a Calabi-Yau. We consider the various possible geometric transitions of the 3-fold and show that they correspond to Seiberg-like dualities (represented by Weyl reflections in the A-D-E case or `mutations' of bundles in the case of vanishing 4-cycles) or large N dualities involving gaugino condensates (generalized conifold transitions). Also duality cascades are naturally realized in these classes of theories, and are related to the affine Weyl group symmetry in the A-D-E case.

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F. Cachazo, B. Fiol, K. Intriligator, S. Katz, C. Vafa. 2002-01-19. A Geometric Unification of Dualities. https://doi.org/10.1016/s0550-3213(02)00078-0

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