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Topological strings, strips and quivers

Panfil, Miłosz and Sułkowski, Piotr (2019) Topological strings, strips and quivers. Journal of High Energy Physics, 2019 (1). Art. No. 124. ISSN 1126-6708.

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We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities that characterize open topological string theory on these manifolds, such as partition functions, Gromov-Witten invariants, or open BPS invariants, can be expressed in terms of characteristics of the moduli space of representations of the corresponding quiver. This has various deep consequences; in particular, expressing open BPS invariants in terms of motivic Donaldson-Thomas invariants, immediately proves integrality of the former ones. Taking advantage of the relation to quivers we also derive explicit expressions for classical open BPS invariants for an arbitrary strip geometry, which lead to a large set of number theoretic integrality statements. Furthermore, for a specific framing, open topological string partition functions for strip geometries take form of generalized q-hypergeometric functions, which leads to a novel representation of these functions in terms of quantum dilogarithms and integral invariants. We also study quantum curves and A-polynomials associated to quivers, various limits thereof, and their specializations relevant for strip geometries. The relation between toric manifolds and quivers can be regarded as a generalization of the knots-quivers correspondence to more general Calabi-Yau geometries.

Item Type:Article
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URLURL TypeDescription Paper
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 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: November 19, 2018; Accepted: January 10, 2019; Published: January 15, 2019. We thank Tobias Ekholm, Sergei Gukov, Piotr Kucharski, Hélder Larragível, Chiu-Chu Melissa Liu, Pietro Longhi, Marko Stošić, Cumrun Vafa, Johannes Walcher, and Don Zagier for inspiring discussions. P.S. thanks Aspen Center for Physics, Simons Center for Geometry and Physics, International Centre for Theoretical Sciences in Bangalore, Banff International Research Station, and Kavli Institute for Theoretical Physics at the University of California Santa Barbara, where parts of this work were done, for hospitality. 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, the Foundation for Polish Science, in part by the National Science Foundation under Grant No. PHY-1748958, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. M.P. acknowledges the support from the National Science Centre through the FUGA grant 2015/16/S/ST2/00448.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
Foundation for Polish ScienceUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
National Science Centre (Poland)2015/16/S/ST2/00448
Subject Keywords:M-Theory, Topological Field Theories, Topological Strings
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Issue or Number:1
Record Number:CaltechAUTHORS:20181119-151313162
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Official Citation:Panfil, M. & Sułkowski, P. J. High Energ. Phys. (2019) 2019: 124.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91034
Deposited By: Joy Painter
Deposited On:19 Nov 2018 23:19
Last Modified:11 Feb 2020 19:10

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