Topological strings, strips and quivers
Abstract
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-quiversmore »
- Authors:
-
- Univ. of Warsaw (Poland)
- Univ. of Warsaw (Poland); California Institute of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); Foundation for Polish Science; National Science Foundation (NSF); National Science Centre
- OSTI Identifier:
- 1611634
- Grant/Contract Number:
- SC0011632; 2015/16/S/ST2/00448; PHY-1748958; 335739
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 1; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics; M-Theory; Topological Field Theories; Topological Strings
Citation Formats
Panfil, Miłosz, and Sułkowski, Piotr. Topological strings, strips and quivers. United States: N. p., 2019.
Web. doi:10.1007/jhep01(2019)124.
Panfil, Miłosz, & Sułkowski, Piotr. Topological strings, strips and quivers. United States. https://doi.org/10.1007/jhep01(2019)124
Panfil, Miłosz, and Sułkowski, Piotr. Tue .
"Topological strings, strips and quivers". United States. https://doi.org/10.1007/jhep01(2019)124. https://www.osti.gov/servlets/purl/1611634.
@article{osti_1611634,
title = {Topological strings, strips and quivers},
author = {Panfil, Miłosz and Sułkowski, Piotr},
abstractNote = {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.},
doi = {10.1007/jhep01(2019)124},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2019,
place = {United States},
year = {Tue Jan 15 00:00:00 EST 2019},
month = {Tue Jan 15 00:00:00 EST 2019}
}
Web of Science
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