All-order differential equations for one-loop closed-string integrals and modular graph forms

A bstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of t...

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Veröffentlicht in:The journal of high energy physics Jg. 2020; H. 1; S. 64 - 74
Hauptverfasser: Gerken, Jan E., Kleinschmidt, Axel, Schlotterer, Oliver
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 2020
Springer Nature B.V
SpringerOpen
Schlagworte:
Conformal Field Models in String Theory
Differential equations
High energy physics
Integrals
Laplace equation
Mathematical analysis
Regular Article - Theoretical Physics
Scattering Amplitudes
Strings
Superstrings and Heterotic Strings
Toruses
Scattering Amplitudes
Superstrings and Heterotic Strings
Conformal Field Models in String Theory
ISSN:1029-8479, 1126-6708, 1029-8479
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Abstract A bstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
AbstractList We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
Abstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
A bstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and second-order Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first- and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals.
ArticleNumber 64
Author Kleinschmidt, Axel
Gerken, Jan E.
Schlotterer, Oliver
Author_xml – sequence: 1
  givenname: Jan E.
  orcidid: 0000-0002-0172-7944
  surname: Gerken
  fullname: Gerken, Jan E.
  email: jan.gerken@aei.mpg.de
  organization: Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut
– sequence: 2
  givenname: Axel
  surname: Kleinschmidt
  fullname: Kleinschmidt, Axel
  organization: Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, International Solvay Institutes ULB-Campus Plaine CP231
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  givenname: Oliver
  orcidid: 0000-0002-1048-661X
  surname: Schlotterer
  fullname: Schlotterer, Oliver
  organization: Department of Physics and Astronomy, Uppsala University
BackLink https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-407290$$DView record from Swedish Publication Index (Uppsala universitet)
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Keywords Scattering Amplitudes
Superstrings and Heterotic Strings
Conformal Field Models in String Theory
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Snippet A bstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and...
We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II...
Abstract We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and...
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SubjectTerms Conformal Field Models in String Theory
Differential equations
High energy physics
Integrals
Laplace equation
Mathematical analysis
Regular Article - Theoretical Physics
Scattering Amplitudes
Strings
Superstrings and Heterotic Strings
Toruses
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Title All-order differential equations for one-loop closed-string integrals and modular graph forms
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