From Modular Graph Forms to Iterated Integrals
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911146486792192 |
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| author | Claasen, Emiel Doroudiani, Mehregan |
| author_facet | Claasen, Emiel Doroudiani, Mehregan |
| contents | 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 \textsc{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 superstring amplitude at eighth order in the inverse string tension $α^{\prime 8}$, which we use to calculate the $α^{\prime 8}ζ_3ζ_5$ contribution to the analytic part of the amplitude. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_05531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Modular Graph Forms to Iterated Integrals Claasen, Emiel Doroudiani, Mehregan High Energy Physics - Theory 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 \textsc{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 superstring amplitude at eighth order in the inverse string tension $α^{\prime 8}$, which we use to calculate the $α^{\prime 8}ζ_3ζ_5$ contribution to the analytic part of the amplitude. |
| title | From Modular Graph Forms to Iterated Integrals |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.05531 |