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Quiver Yangian and Supersymmetric Quantum Mechanics

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arxiv 2008.07006 v2 pith:L2ACOBD7 submitted 2020-08-16 hep-th math.AGmath.QAmath.RT

Dmitry Galakhov , Masahito Yamazaki This is my paper · ORCID
classification hep-thmath.AGmath.QAmath.RT
keywords mechanicsquantumquiveralgebraconfigurationssupersymmetricyangianaction
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The statistical model of crystal melting represents BPS configurations of D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently on the crystal-melting configurations. We physically derive the algebra and its action on the BPS states, starting with the effective supersymmetric quiver quantum mechanics on the D-brane worldvolume. This leads to remarkable combinatorial identities involving equivariant integrations on the moduli space of the quantum mechanics, which can be checked by numerical computations.

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Cited by 3 Pith papers

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

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

    hep-th 2025-01 conditional novelty 7.0 of 10

    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...

  2. 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.

  3. 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.

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