A geometric unification of dualities

 
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Cachazo, F.
Fiol, B.
Intriligator, K.
Katz, S.
Vafa, C.
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https://doi.org/10.1016/S0550-3213(02)00078-0
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Cachazo, F., B. Fiol, K. Intriligator, S. Katz, and C. Vafa. 2002. “A Geometric Unification of Dualities.” Nuclear Physics B 628 (1–2): 3–78. https://doi.org/10.1016/s0550-3213(02)00078-0.
Abstract
We study the dynamics of a large class of A = I quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau three-folds. These include V = 2 (affine) A-D-E quiver theories deformed by superpotential terms, as well as chiral A = I 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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http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385085

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