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Knots-quivers correspondence

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arxiv 1707.04017 v1 pith:JLQ5T7CV submitted 2017-07-13 hep-th math-phmath.GNmath.MPmath.QA

Piotr Kucharski , Markus Reineke , Marko Stosic , Piotr Su{l}kowski This is my paper · ORCID
classification hep-thmath-phmath.GNmath.MPmath.QA
keywords knotsidentifyquiverspropertiesquiversomevariousassociated
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We introduce and explore the relation between knot invariants and quiver representation theory, which follows from the identification of quiver quantum mechanics in D-brane systems representing knots. We identify various structural properties of quivers associated to knots, and identify such quivers explicitly in many examples, including some infinite families of knots, all knots up to 6 crossings, and some knots with thick homology. Moreover, based on these properties, we derive previously unknown expressions for colored HOMFLY-PT polynomials and superpolynomials for various knots. For all knots, for which we identify the corresponding quivers, the LMOV conjecture for all symmetric representations (i.e. integrality of relevant BPS numbers) is automatically proved.

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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. 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}.

  2. Wild wall-crossing and symmetric quivers in 4d and 3d $\mathcal{N}=2$ field theories

    hep-th 2025-06 conditional novelty 6.0 of 10

    The paper derives a tree-of-unlinkings formula for wild Donaldson-Thomas invariants of m-Kronecker quivers from wall-crossing identities rewritten through symmetric quivers and diagonalization.

  3. Quantum invariants of 3-manifolds and links: a review

    math-ph 2025-09 unverdicted novelty 1.0 of 10

    This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.

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