Open topological recursion relations in genus 1 and integrable systems

Open topological recursion relations in genus 1 and integrable systems

Abstract The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent...

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Main Authors: Oscar Brauer Gomez, Alexandr Buryak
Format: Article
Language:English
Published: SpringerOpen 2021-01-01
Series:Journal of High Energy Physics
Subjects:
Integrable Hierarchies
Differential and Algebraic Geometry
Topological Field Theories
Online Access:https://doi.org/10.1007/JHEP01(2021)048
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spelling doaj-9c43974d0ca340f69b665fa9851ccbd32021-01-17T12:07:06ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021111510.1007/JHEP01(2021)048Open topological recursion relations in genus 1 and integrable systemsOscar Brauer Gomez0Alexandr Buryak1School of Mathematics, University of LeedsFaculty of Mathematics, National Research University Higher School of EconomicsAbstract The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation up to genus 1 the exponent of an open descendent potential satisfies a system of explicitly constructed linear evolutionary PDEs with one spatial variable.https://doi.org/10.1007/JHEP01(2021)048Integrable HierarchiesDifferential and Algebraic GeometryTopological Field Theories
collection DOAJ
language English
format Article
sources DOAJ
author Oscar Brauer Gomez
Alexandr Buryak
spellingShingle Oscar Brauer Gomez
Alexandr Buryak
Open topological recursion relations in genus 1 and integrable systems
Journal of High Energy Physics
Integrable Hierarchies
Differential and Algebraic Geometry
Topological Field Theories
author_facet Oscar Brauer Gomez
Alexandr Buryak
author_sort Oscar Brauer Gomez
title Open topological recursion relations in genus 1 and integrable systems
title_short Open topological recursion relations in genus 1 and integrable systems
title_full Open topological recursion relations in genus 1 and integrable systems
title_fullStr Open topological recursion relations in genus 1 and integrable systems
title_full_unstemmed Open topological recursion relations in genus 1 and integrable systems
title_sort open topological recursion relations in genus 1 and integrable systems
publisher SpringerOpen
series Journal of High Energy Physics
issn 1029-8479
publishDate 2021-01-01
description Abstract The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation up to genus 1 the exponent of an open descendent potential satisfies a system of explicitly constructed linear evolutionary PDEs with one spatial variable.
topic Integrable Hierarchies
Differential and Algebraic Geometry
Topological Field Theories
url https://doi.org/10.1007/JHEP01(2021)048
work_keys_str_mv AT oscarbrauergomez opentopologicalrecursionrelationsingenus1andintegrablesystems
AT alexandrburyak opentopologicalrecursionrelationsingenus1andintegrablesystems
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