Modular graph forms from equivariant iterated Eisenstein integrals

Dorigoni, Daniele; Doroudiani, Mehregan; Drewitt, Joshua; Hidding, Martijn; Kleinschmidt, Axel; Matthes, Nils; Schlotterer, Oliver; Verbeek, Bram

Abstract

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown’s alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown’s conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown’s construction fully explicit to all orders.

Citation

Dorigoni, D., Doroudiani, M., Drewitt, J., Hidding, M., Kleinschmidt, A., Matthes, N., …Verbeek, B. (2022). Modular graph forms from equivariant iterated Eisenstein integrals. Journal of High Energy Physics, 2022(12), https://doi.org/10.1007/jhep12%282022%29162

• Journal Article Type: Article
• Acceptance Date: Dec 1, 2022
• Online Publication Date: Dec 28, 2022
• Publication Date: 2022
• Deposit Date: Jan 23, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 12
• DOI: https://doi.org/10.1007/jhep12%282022%29162