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Toroidal and Elliptic Quiver BPS Algebras and Beyond

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arxiv 2108.10286 v2 pith:BJB37W5D submitted 2021-08-23 hep-th math.ATmath.QAmath.RT

Dmitry Galakhov , Wei Li , Masahito Yamazaki This is my paper · ORCID
classification hep-thmath.ATmath.QAmath.RT
keywords algebrasquiverelliptictheoriestoroidalalgebragaugerepresentations
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abstract

The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

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Cited by 4 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. Super-Hamiltonians for super-Macdonald polynomials

    hep-th 2025-01 conditional novelty 6.0 of 10

    Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.

  4. Gauge Origami and BPS/CFT correspondence

    hep-th 2025-02 conditional novelty 5.0 of 10

    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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