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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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| 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. |
| format | Article |
| id | doaj-art-de298d5deb094f0492bb887af619dfd9 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| 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 |