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Nahm sums, quiver A-polynomials and topological recursion

Larraguível, Hélder and Noshchenko, Dmitry and Panfil, Miłosz and Sułkowski, Piotr (2020) Nahm sums, quiver A-polynomials and topological recursion. Journal of High Energy Physics, 2020 (7). Art. No. 151. ISSN 1029-8479. doi:10.1007/jhep07(2020)151.

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We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Larraguível, Hélder0000-0002-2894-5052
Panfil, Miłosz0000-0003-1525-4700
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: May 14, 2020; Accepted: June 11, 2020; Published: July 22, 2020. We thank Bertrand Eynard, Sergei Gukov, Piotr Kucharski and Marko Stošić for discussions, correspondence, and comments on the manuscript. This work has been 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 TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). MP acknowledges the support from the National Science Centre, Poland, in the initial phase of the project under the FUGA grant 2015/16/S/ST2/00448 and in the final phase of the project under the SONATA grant 2018/31/D/ST3/03588.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
European Regional Development FundPOIR.04.04.00-00-5C55/17-00
National Science Centre (Poland)2015/16/S/ST2/00448
National Science Centre (Poland)2018/31/D/ST3/03588
Subject Keywords:Matrix Models; Topological Strings; Differential and Algebraic Geometry
Issue or Number:7
Record Number:CaltechAUTHORS:20200724-120421685
Persistent URL:
Official Citation:Larraguível, H., Noshchenko, D., Panfil, M. et al. Nahm sums, quiver A-polynomials and topological recursion. J. High Energ. Phys. 2020, 151 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104567
Deposited By: Tony Diaz
Deposited On:24 Jul 2020 19:29
Last Modified:16 Nov 2021 18:33

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