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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Vydané v:	The journal of high energy physics Ročník 2019; číslo 1; s. 1 - 45
Hlavní autori:	Panfil, Miłosz, Sułkowski, Piotr
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019 Springer Nature B.V Springer Berlin SpringerOpen
Predmet:	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
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Abstract	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.
AbstractList	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. 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. 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-quivers correspondence to more general Calabi-Yau geometries. 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.
ArticleNumber	124
Author	Panfil, Miłosz Sułkowski, Piotr
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Cites_doi	10.1112/S0010437X12000152 10.1007/JHEP03(2016)004 10.1215/00127094-2017-0030 10.1007/s00220-013-1789-8 10.1007/s00220-016-2682-z 10.4310/ATMP.2006.v10.n3.a2 10.1080/10236190701264925 10.1007/JHEP07(2017)032 10.1007/JHEP08(2017)063 10.4310/ATMP.2014.v18.n4.a3 10.1016/S0550-3213(00)00118-8 10.1007/s00220-005-1448-9 10.1007/s002200100374 10.1112/S0010437X1000521X 10.4310/CNTP.2011.v5.n2.a1 10.1007/JHEP05(2013)166 10.1007/JHEP08(2017)139 10.1016/S0550-3213(00)00761-6 10.1007/JHEP02(2012)070 10.1007/JHEP06(2012)178 10.1007/0-8176-4467-9_16 10.1090/pspum/090/01532 10.1007/s00220-004-1162-z 10.1088/1126-6708/2006/01/040 10.1007/978-3-540-30308-4_2 10.1017/CBO9780511526251 10.4171/dm/359 10.1142/S0218216502001561 10.1088/1126-6708/2000/11/007 10.1007/JHEP11(2016)120 10.1007/s002200050461 10.1007/BF01217730
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Snippet	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... We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact... Abstract We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without...
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SubjectTerms	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
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Title	Topological strings, strips and quivers
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