From modular graph forms to iterated integrals

Abstract Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms into iterated integrals of holomorph...

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Main Authors: E. Claasen, M. Doroudiani
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP06(2025)204
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author E. Claasen
M. Doroudiani
author_facet E. Claasen
M. Doroudiani
author_sort E. Claasen
collection DOAJ
description Abstract Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms into iterated integrals of holomorphic Eisenstein series and provide a Mathematica package that implements all modular graph form topologies up to four vertices. To achieve this, we introduce specific tree-representations of modular graph forms. The presented method enables the conversion of the integrand of the four-graviton one-loop amplitude in Type II superstring theory at eighth order in the inverse string tension α ′8, which we use to calculate the α ′8 ζ 3 ζ 5 contribution to the analytic part of the amplitude.
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issn 1029-8479
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spelling doaj-art-de298d5deb094f0492bb887af619dfd92025-08-20T03:04:21ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025613410.1007/JHEP06(2025)204From modular graph forms to iterated integralsE. Claasen0M. Doroudiani1Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)School of Physics & Astronomy, University of SouthamptonAbstract Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms into iterated integrals of holomorphic Eisenstein series and provide a Mathematica package that implements all modular graph form topologies up to four vertices. To achieve this, we introduce specific tree-representations of modular graph forms. The presented method enables the conversion of the integrand of the four-graviton one-loop amplitude in Type II superstring theory at eighth order in the inverse string tension α ′8, which we use to calculate the α ′8 ζ 3 ζ 5 contribution to the analytic part of the amplitude.https://doi.org/10.1007/JHEP06(2025)204Scattering AmplitudesSuperstrings and Heterotic Strings
spellingShingle E. Claasen
M. Doroudiani
From modular graph forms to iterated integrals
Journal of High Energy Physics
Scattering Amplitudes
Superstrings and Heterotic Strings
title From modular graph forms to iterated integrals
title_full From modular graph forms to iterated integrals
title_fullStr From modular graph forms to iterated integrals
title_full_unstemmed From modular graph forms to iterated integrals
title_short From modular graph forms to iterated integrals
title_sort from modular graph forms to iterated integrals
topic Scattering Amplitudes
Superstrings and Heterotic Strings
url https://doi.org/10.1007/JHEP06(2025)204
work_keys_str_mv AT eclaasen frommodulargraphformstoiteratedintegrals
AT mdoroudiani frommodulargraphformstoiteratedintegrals