Topological strings, strips and quivers

A bstract 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...

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Published in:The journal of high energy physics Vol. 2019; no. 1; pp. 1 - 45
Main Authors: Panfil, Miłosz, Sułkowski, Piotr
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019
Springer Nature B.V
Springer Berlin
SpringerOpen
Subjects:
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Hypergeometric functions
Invariants
Knots
M-Theory
Manifolds (mathematics)
Mathematical analysis
Partitions
Partitions (mathematics)
Physics
Physics and Astronomy
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Representations
String Theory
Strings
Strip
Topological Field Theories
Topological Strings
Topological Strings
Topological Field Theories
M-Theory
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract 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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USDOE Office of Science (SC), High Energy Physics (HEP)
National Science Foundation (NSF)
SC0011632; 2015/16/S/ST2/00448; PHY-1748958; 335739
Foundation for Polish Science
National Science Centre
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2019)124