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BPS states, knots and quivers

Kucharski, Piotr and Reineke, Markus and Stošić, Marko and Sułkowski, Piotr (2017) BPS states, knots and quivers. Physical Review D, 96 (12). Art. No. 121902. ISSN 2470-0010. doi:10.1103/PhysRevD.96.121902.

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We argue how to identify the supersymmetric quiver quantum mechanics description of BPS states, which arise in string theory in brane systems representing knots. This leads to a surprising relation between knots and quivers: to a given knot, we associate a quiver, so that various types of knot invariants are expressed in terms of characteristics of a moduli space of representations of the corresponding quiver. This statement can be regarded as a novel type of categorification of knot invariants, and among its various consequences we find that Labastida-Mariño-Ooguri-Vafa (LMOV) invariants of a knot can be expressed in terms of motivic Donaldson-Thomas invariants of the corresponding quiver; this proves integrality of LMOV invariants (once the corresponding quiver is identified), conjectured originally based on string theory and M-theory arguments.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kucharski, Piotr0000-0002-9599-5658
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2017 American Physical Society. Received 1 March 2017; published 27 December 2017. We thank Sergei Gukov, Satoshi Nawata, Miłosz Panfil, Yan Soibelman, Richard Thomas, Cumrun Vafa, and Paul Wedrich for discussions and comments on the manuscript. This work is supported by the ERC Starting Grant No. 335739 “Quantum fields and knot homologies” funded by the European Research Council under the European Union’s Seventh Framework Programme, and the Foundation for Polish Science. M. S. is partially supported by the Ministry of Science of Serbia, Project No. 174012, and by Fundação para a Ciência e a Tecnologia (FCT), through the FCT Investigador Grant.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Foundation for Polish ScienceUNSPECIFIED
Ministry of Science (Serbia)174012
Fundação para a Ciência e a Tecnologia (FCT)UNSPECIFIED
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Issue or Number:12
Record Number:CaltechAUTHORS:20170713-144921183
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79096
Deposited By: Joy Painter
Deposited On:14 Jul 2017 14:48
Last Modified:15 Nov 2021 17:45

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