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Title: 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 » correspondence to more general Calabi-Yau geometries.« less

Authors:
ORCiD logo [1];  [2]
  1. Univ. of Warsaw (Poland)
  2. 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}
}

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Works referenced in this record:

Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants
journal, February 2011


The Topological Vertex
journal, September 2004

  • Aganagic, Mina; Klemm, Albrecht; Mari�o, Marcos
  • Communications in Mathematical Physics, Vol. 254, Issue 2
  • DOI: 10.1007/s00220-004-1162-z

A-polynomial, B-model, and quantization
journal, February 2012


Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants
journal, January 2011


BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

  • Alim, Murad; Cecotti, Sergio; Córdova, Clay
  • Communications in Mathematical Physics, Vol. 323, Issue 3
  • DOI: 10.1007/s00220-013-1789-8

Properties of q -holonomic functions
journal, July 2007

  • Koepf, Wolfram; Rajković, Predrag M.; Marinković, Sladjana D.
  • Journal of Difference Equations and Applications, Vol. 13, Issue 7
  • DOI: 10.1080/10236190701264925

Topological strings, D-model, and knot contact homology
journal, January 2014

  • Vafa, Cumrun; Aganagic, Mina; Ekholm, Tobias
  • Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 4
  • DOI: 10.4310/ATMP.2014.v18.n4.a3

Knot invariants and topological strings
journal, June 2000


Cohomological Hall algebra of a symmetric quiver
journal, May 2012


A New Point of View in the Theory of Knot and Link Invariants
journal, March 2002

  • Labastida, José M. F.; Mariño, Marcos
  • Journal of Knot Theory and Its Ramifications, Vol. 11, Issue 02
  • DOI: 10.1142/S0218216502001561

On link invariants and topological string amplitudes
journal, April 2001


The colored HOMFLYPT function is $q$ -holonomic
journal, February 2018

  • Garoufalidis, Stavros; Lauda, Aaron D.; Lê, Thang T. Q.
  • Duke Mathematical Journal, Vol. 167, Issue 3
  • DOI: 10.1215/00127094-2017-0030

Vertices, vortices & interacting surface operators
journal, June 2012

  • Bonelli, Giulio; Tanzini, Alessandro; Zhao, Jian
  • Journal of High Energy Physics, Vol. 2012, Issue 6
  • DOI: 10.1007/JHEP06(2012)178

On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
journal, May 2013

  • Manschot, Jan; Pioline, Boris; Sen, Ashoke
  • Journal of High Energy Physics, Vol. 2013, Issue 5
  • DOI: 10.1007/JHEP05(2013)166

Polynomial Invariants for Torus Knots¶and Topological Strings
journal, March 2001

  • Labastida, J. M. F.; Mariño, Marcos
  • Communications in Mathematical Physics, Vol. 217, Issue 2
  • DOI: 10.1007/s002200100374

Exponential networks and representations of quivers
journal, August 2017

  • Eager, Richard; Selmani, Sam Alexandre; Walcher, Johannes
  • Journal of High Energy Physics, Vol. 2017, Issue 8
  • DOI: 10.1007/JHEP08(2017)063

Knot invariants and Calabi-Yau crystals
journal, January 2006


BPS graphs: from spectral networks to BPS quivers
journal, July 2017

  • Gabella, Maxime; Longhi, Pietro; Park, Chan Y.
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)032

Knots, BPS States, and Algebraic Curves
journal, July 2016

  • Garoufalidis, Stavros; Kucharski, Piotr; Sułkowski, Piotr
  • Communications in Mathematical Physics, Vol. 346, Issue 1
  • DOI: 10.1007/s00220-016-2682-z

Basic hypergeometric series
journal, September 1991


The vertex on a strip
journal, January 2006

  • Iqbal, Amer; Kashani-Poor, Amir-Kian
  • Advances in Theoretical and Mathematical Physics, Vol. 10, Issue 3
  • DOI: 10.4310/ATMP.2006.v10.n3.a2

On the Algebras of BPS States
journal, October 1998

  • Harvey, Jeffrey A.; Moore, Gregory
  • Communications in Mathematical Physics, Vol. 197, Issue 3
  • DOI: 10.1007/s002200050461

Checks of integrality properties in topological strings
journal, August 2017

  • Mironov, A.; Morozov, A.; Morozov, An.
  • Journal of High Energy Physics, Vol. 2017, Issue 8
  • DOI: 10.1007/JHEP08(2017)139

Topological Strings and Integrable Hierarchies
journal, October 2005

  • Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht
  • Communications in Mathematical Physics, Vol. 261, Issue 2
  • DOI: 10.1007/s00220-005-1448-9

Sequencing BPS spectra
journal, March 2016

  • Gukov, Sergei; Nawata, Satoshi; Saberi, Ingmar
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)004

Quantum field theory and the Jones polynomial
journal, September 1989

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 121, Issue 3
  • DOI: 10.1007/BF01217730

Knots, links and branes at large N
journal, November 2000


BPS counting for knots and combinatorics on words
journal, November 2016

  • Kucharski, Piotr; Sułkowski, Piotr
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)120

Cohomological Hall algebra of a symmetric quiver
text, January 2011


Knots, BPS states, and algebraic curves
text, January 2015


Sequencing BPS Spectra
text, January 2015


The colored HOMFLYPT function is $q$-holonomic
text, January 2016


BPS Graphs: From Spectral Networks to BPS Quivers
text, January 2017


On Link Invariants and Topological String Amplitudes
text, January 2000


Topological Strings and Integrable Hierarchies
text, January 2003


The Vertex on a Strip
text, January 2004


On the algebras of BPS states
text, January 1996


Topological Strings and Integrable Hierarchies
text, January 2003


Works referencing / citing this record:

Multi-cover skeins, quivers, and 3d $$ \mathcal{N} $$ = 2 dualities
journal, February 2020

  • Ekholm, Tobias; Kucharski, Piotr; Longhi, Pietro
  • Journal of High Energy Physics, Vol. 2020, Issue 2
  • DOI: 10.1007/jhep02(2020)018

Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities
text, January 2019


Quivers for 3-manifolds: the correspondence, BPS states, and 3d $$ \mathcal{N} $$ = 2 theories
journal, September 2020


On explicit formulae of LMOV invariants
journal, October 2019


Tangle addition and the knots‐quivers correspondence
journal, January 2021

  • Stošić, Marko; Wedrich, Paul
  • Journal of the London Mathematical Society, Vol. 104, Issue 1
  • DOI: 10.1112/jlms.12433