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Symmetries of Toric Duality

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arxiv hep-th/0205144 v3 pith:G5QL6TQH submitted 2002-05-15 hep-th

Bo Feng , Sebastian Franco , Amihay Hanany , Yang-Hui He This is my paper · ORCID
classification hep-th
keywords dualitysymmetriescertainsymmetrytoriccasesmultiplicitiesmultiplicity
verification ladder T0 review T1 audit T2 compute T3 formal
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This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.

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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. Tilting Mutations and Quiver-Invariant Dualities in Brane Tilings

    hep-th 2026-08 conditional novelty 6.0 of 10

    Three families of tilting mutations on brane tilings produce quiver-invariant dualities, linking five doublets and one triplet of toric phases of H^{1,1,2,1}.

  3. 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.

  4. 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}.

  5. 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.

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