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A Geometric Unification of Dualities

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arxiv hep-th/0110028 v2 pith:JKJU7YOM submitted 2001-10-02 hep-th

F. Cachazo , B. Fiol , K. Intriligator , S. Katz , C. Vafa This is my paper · ORCID
classification hep-th
keywords theoriesa-d-ecasecyclesdualitiesquiveraffinecalabi-yau
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 3 Pith papers

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  1. Abelian Orbifolds for Brane Brick Models

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.

  2. A class of half-BPS boundary conditions for $A_{K-1}$ circular quivers

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Characterizes solutions to BPS equations for D4-branes ending on boundary D6-branes in A_{K-1} circular quivers, finding a winding phenomenon absent in linear quivers and proposing the maximal-winding case as S-dual t...

  3. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

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