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Brane Dimers and Quiver Gauge Theories

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arxiv hep-th/0504110 v2 pith:P6AVWT5O submitted 2005-04-13 hep-th

Sebastian Franco , Amihay Hanany , Kristian D. Kennaway , David Vegh , Brian Wecht This is my paper · ORCID
classification hep-th
keywords quivertheoriesbranegaugetoriccalabi-yaucentralcomputations
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We describe a technique which enables one to quickly compute an infinite number of toric geometries and their dual quiver gauge theories. The central object in this construction is a ``brane tiling,'' which is a collection of D5-branes ending on an NS5-brane wrapping a holomorphic curve that can be represented as a periodic tiling of the plane. This construction solves the longstanding problem of computing superpotentials for D-branes probing a singular non-compact toric Calabi-Yau manifold, and overcomes many difficulties which were encountered in previous work. The brane tilings give the largest class of N=1 quiver gauge theories yet studied. A central feature of this work is the relation of these tilings to dimer constructions previously studied in a variety of contexts. We do many examples of computations with dimers, which give new results as well as confirm previous computations. Using our methods we explicitly derive the moduli space of the entire Y^{p,q} family of quiver theories, verifying that they correspond to the appropriate geometries. Our results may be interpreted as a generalization of the McKay correspondence to non-compact 3-dimensional toric Calabi-Yau manifolds.

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Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 308 citations worldwide. 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

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    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. Dimers for Relativistic Toda Models with Reflective Boundaries

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    Dimer graphs are constructed for relativistic Toda chains of listed Lie algebra types, and Seiberg-Witten curves of 5d N=1 pure SYM for group G are identified as spectral curves of the dual Toda chain for G^vee.

  4. $Q$-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.

  5. Planar Abelian Duals of Chern-Simons QCD

    hep-th 2025-06 conditional novelty 7.0 of 10

    Proposes a new family of infrared dualities between non-Abelian 3d Chern-Simons QCD and Abelian planar quiver theories, with a bosonization rule trading flavors for quiver columns.

  6. On the Origin of Toric Diagrams

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    A field's scaling dimension equals the number of perfect matchings at the chosen origin that contain it, making the gauge-theory Hilbert series equal the Ehrhart series of the dual polytope.

  7. Quiver-Invariant Dualities between Brane Tilings

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    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.

  8. Quiver superconformal index and giant gravitons: asymptotics and expansions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.

  9. 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.

  10. Machine Learning Toric Duality in Brane Tilings

    hep-th 2024-09 unverdicted novelty 5.0 of 10

    Neural networks classify Seiberg dual classes on Z_m x Z_n orbifolds with R^2=0.988 and predict toric multiplicities for Y^{6,0} with mean absolute error 0.021 under fixed Kasteleyn representative.

  11. A Crash Course in Supersymmetric Field Theory Across Dimensions

    hep-th 2026-07 unverdicted novelty 2.0 of 10

    Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.

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