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
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP01(2020)064