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

Gerken, J. E., Kleinschmidt, A., & Schlotterer, O. (2020). All-order differential equations for one-loop closed-string integrals and modular graph forms. Journal of High Energy Physics, 2020 (1): 64. doi:10.1007/JHEP01(2020)064.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-4D24-D Version Permalink: http://hdl.handle.net/21.11116/0000-0005-A5AF-C
Genre: Journal Article

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 Creators:
Gerken, Jan E.1, Author              
Kleinschmidt, Axel2, Author              
Schlotterer, Oliver, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT
 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.

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 Dates: 2019-11-082020
 Publication Status: Published in print
 Pages: 54+24 pages
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 Rev. Method: -
 Identifiers: arXiv: 1911.03476
URI: http://arxiv.org/abs/1911.03476
DOI: 10.1007/JHEP01(2020)064
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Title: Journal of High Energy Physics
Source Genre: Journal
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Pages: - Volume / Issue: 2020 (1) Sequence Number: 64 Start / End Page: - Identifier: -