A geometric unification of dualities

F. Cachazo; B. Fiol; K. Intriligator; S. Katz; C. Vafa

doi:10.1016/S0550-3213(02)00078-0

A geometric unification of dualities

F. Cachazo, B. Fiol, K. Intriligator, S. Katz, C. Vafa

Research output: Contribution to journal › Article › peer-review

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 three-folds. 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 Wey1 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 Wey1 group symmetry in the A-D-E case.

Original language	English (US)
Pages (from-to)	3-78
Number of pages	76
Journal	Nuclear Physics B
Volume	628
Issue number	1-2
DOIs	https://doi.org/10.1016/S0550-3213(02)00078-0
State	Published - Apr 29 2002

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Nuclear and High Energy Physics

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title = "A geometric unification of dualities",

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 three-folds. 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 Wey1 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 Wey1 group symmetry in the A-D-E case.",

author = "F. Cachazo and B. Fiol and K. Intriligator and S. Katz and C. Vafa",

note = "Funding Information: The research of F.C. and C.V. is supported in part by NSF grants PHY-9802709 and DMS-0074329. The research of B.F. is supported by a Marie Curie fellowship, and also by the IRF Centers of Excellence program, by the European RTN network HPRN-CT-2000-00122, and by Minerva. The research of K.I. is supported by DOE-FG03-97ER40546. The research of S.K. is supported in part by NSF grant DMS-073657 and NSA grant MDA904-00-1-052.",

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AU - Fiol, B.

AU - Intriligator, K.

AU - Katz, S.

AU - Vafa, C.

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Y1 - 2002/4/29

N2 - 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 three-folds. 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 Wey1 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 Wey1 group symmetry in the A-D-E case.

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A geometric unification of dualities

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