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Permutohedra for knots and quivers

Jankowski, Jakub and Kucharski, Piotr and Larraguível, Hélder and Noshchenko, Dmitry and Sułkowski, Piotr (2021) Permutohedra for knots and quivers. Physical Review D, 104 (8). Art. No. 086017. ISSN 2470-0010. doi:10.1103/physrevd.104.086017.

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The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be assigned to a given knot and encode the same information. In this work we study this phenomenon systematically and show that it is generic rather than exceptional. First, we find conditions that characterize equivalent quivers. Then we show that equivalent quivers arise in families that have the structure of permutohedra, and the set of all equivalent quivers for a given knot is parametrized by vertices of a graph made of several permutohedra glued together. These graphs can be also interpreted as webs of dual three-dimensional N = 2 theories. All these results are intimately related to properties of homological diagrams for knots, as well as to multicover skein relations that arise in the counting of holomorphic curves with boundaries on Lagrangian branes in Calabi-Yau three-folds.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Jankowski, Jakub0000-0003-0830-5346
Kucharski, Piotr0000-0002-9599-5658
Larraguível, Hélder0000-0002-2894-5052
Noshchenko, Dmitry0000-0002-9639-5603
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. (Received 4 June 2021; accepted 9 July 2021; published 12 October 2021) We thank Tobias Ekholm, Angus Gruen, Sergei Gukov, Pietro Longhi, Sunghyuk Park, and Marko Stošić for insightful discussions and comments on the manuscript. The work of J. J. was supported by the Polish National Science Centre (NCN) Grant No. 2016/23/D/ST2/03125. P. K. is supported by the Polish Ministry of Education and Science through its program Mobility Plus (decision No. 1667/MOB/V/2017/0). The work of H. L., D. N., and P. S. is supported by the TEAM programme of the Foundation for Polish Science cofinanced by the European Union under the European Regional Development Fund (No. POIR.04.04.00-00-5C55/17-00).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
National Science Centre (Poland)2016/23/D/ST2/03125
Ministry of Education and Science (Poland)1667/MOB/V/2017/0
Foundation for Polish ScienceUNSPECIFIED
European Regional Development FundPOIR.04.04.00-00-5C55/17-00
Issue or Number:8
Record Number:CaltechAUTHORS:20211014-212146719
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111458
Deposited By: George Porter
Deposited On:18 Oct 2021 19:46
Last Modified:18 Oct 2021 19:46

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