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Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters

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arxiv 2411.01987 v2 pith:VXPB4UAT submitted 2024-11-04 hep-th math-phmath.MPmath.QAmath.RT

Taro Kimura , Go Noshita This is my paper · ORCID
classification hep-thmath-phmath.MPmath.QAmath.RT
keywords charactersboundaryconditionsdonaldson--thomasgaugeorigamipartitionquiver
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abstract

We further develop the BPS/CFT correspondence between quiver W-algebras/$qq$-characters and partition functions of gauge origami. We introduce $qq$-characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson--Thomas (DT) $qq$-characters. They are operator versions of the equivariant DT vertices of toric Calabi--Yau three and four-folds. Moreover, we revisit the construction of the D8 $qq$-characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 $qq$-characters with no boundary conditions all commute with each other and discuss its physical interpretation.

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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. Gauge origami on broken lines

    math.AG 2025-02 conditional novelty 6.0 of 10

    The gauge origami partition function on broken lines equals a plethystic exponential and factorizes into rank-one contributions.

  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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