Topological strings, strips and quivers

Panfil, Miłosz; Sułkowski, Piotr

doi:10.1007/jhep01(2019)124

Title: Topological strings, strips and quivers

Journal Article · Tue Jan 15 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2019)124· OSTI ID:1611634

^[1]; Sułkowski, Piotr ^[2]

Univ. of Warsaw (Poland)
Univ. of Warsaw (Poland); California Institute of Technology (CalTech), Pasadena, CA (United States)

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.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Foundation for Polish Science; National Science Foundation (NSF); National Science Centre

Grant/Contract Number:: SC0011632; 2015/16/S/ST2/00448; PHY-1748958; 335739

OSTI ID:: 1611634

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 15 works

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Cited By (5)

Multi-cover skeins, quivers, and 3d $$ \mathcal{N} $$ = 2 dualities Ekholm, Tobias; Kucharski, Piotr; Longhi, Pietro Journal of High Energy Physics, Vol. 2020, Issue 2 https://doi.org/10.1007/jhep02(2020)018	journal	February 2020
Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities Ekholm, Tobias; Kucharski, Piotr; Longhi, Pietro arXiv https://doi.org/10.48550/arxiv.1910.06193	text	January 2019
Quivers for 3-manifolds: the correspondence, BPS states, and 3d $$ \mathcal{N} $$ = 2 theories Kucharski, Piotr Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/jhep09(2020)075	journal	September 2020
On explicit formulae of LMOV invariants Zhu, Shengmao Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)076	journal	October 2019
Tangle addition and the knots‐quivers correspondence Stošić, Marko; Wedrich, Paul Journal of the London Mathematical Society, Vol. 104, Issue 1 https://doi.org/10.1112/jlms.12433	journal	January 2021

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