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Quiver Yangian from Crystal Melting

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arxiv 2003.08909 v3 pith:WD5ILTNK submitted 2020-03-19 hep-th math.AGmath.QAmath.RT

Wei Li , Masahito Yamazaki This is my paper · ORCID
classification hep-thmath.AGmath.QAmath.RT
keywords statescrystalalgebrascalabi-yauconfigurationscyclesmeltingtoric
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abstract

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are "bootstrapped" from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact $4$-cycles.

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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. Charge functions for all dimensional partitions

    math-ph 2025-12 conditional novelty 7.0 of 10

    A conjectured charge-function formula for even-dimensional partitions matches the known 4D case, is proved for 6D, and passes 8D Monte Carlo checks.

  2. Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues

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    For quivers satisfying a no-overlap condition, flavored BPS indices are computed by crystal melting derived from Jeffrey-Kirwan residues, and new double quiver algebras are constructed whose crystal representations en...

  3. Quiver BPS Indices from Crystal Profiles

    hep-th 2026-07 conditional novelty 6.5 of 10

    Elliptic genera and lower-dimensional BPS indices equal discrete sums over molecule boundaries in crystals defined by Jeffrey-Kirwan residues, generalizing Nekrasov Young-diagram formulas.

  4. Weyl Mutations in Quiver Yangians

    hep-th 2026-01 conditional novelty 5.0 of 10

    Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.

  5. Gauge Origami and BPS/CFT correspondence

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    The gauge origami partition function on C4 is realized as a correlation function of BPS qq-character operators, with D6 and D8 characters labeled by plane and solid partitions.

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