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Modular graph forms from equivariant iterated Eisenstein integrals

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


Mehregan Doroudiani

Joshua Drewitt

Martijn Hidding

Axel Kleinschmidt

Nils Matthes

Oliver Schlotterer

Bram Verbeek


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.


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),

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