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Quivers, Tilings, Branes and Rhombi

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arxiv hep-th/0511063 v1 pith:OWGR7LWQ submitted 2005-11-06 hep-th

Amihay Hanany , David Vegh This is my paper · ORCID
classification hep-th
keywords algorithmbranegiventheoriestilingstorica-maximizationangles
verification ladder T0 review T1 audit T2 compute T3 formal
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We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Towards Generalized Dimers for GTPs: $\mathcal{N}=2$ Fractional Branes at Infinite Coupling

    hep-th 2026-07 conditional novelty 7.0 of 10

    N=2 strip condensation — collapsing parallel zig-zag strips in brane tilings — reproduces the expected number of gauge groups and yields GTP quivers related to toric ones by relevant deformations.

  2. 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.

  3. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

  4. Polygonal Quivers

    math.AG 2019-07 unverdicted novelty 7.0 of 10

    Fano lattice polygons define balanced quivers linked to toric surface singularities, placing them on algebraic hypersurfaces with a coinciding generalized mutation operation.

  5. Quiver-Invariant Dualities between Brane Tilings

    hep-th 2026-01 conditional novelty 6.0 of 10

    A tilting mutation of brane tilings yields distinct superpotentials on the same quiver with identical mesonic moduli space, equivalent to a sequence of Seiberg dualities.

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