Authors: Kucharski, Piotr
Reineke, Markus
Stošić, Marko 
Sułkowski, Piotr
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Knots-quivers correspondence
Journal: Advances in Theoretical and Mathematical Physics
Volume: 23
Issue: 7
First page: 1849
Last page: 1902
Issue Date: 1-Jan-2019
Rank: M21
ISSN: 1095-0761
DOI: 10.4310/ATMP.2019.V23.N7.A4
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.
Publisher: International Press
Project: Quantum fields and knot homologies 
Geometry, Education and Visualization With Applications 

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