Modular graph forms from equivariant iterated Eisenstein integrals

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

doi:10.1007/jhep12(2022)162

Modular graph forms from equivariant iterated Eisenstein integrals

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

Authors

Dr Daniele Dorigoni daniele.dorigoni@durham.ac.uk
Associate Professor

Mehregan Doroudiani

Joshua Drewitt

Martijn Hidding

Axel Kleinschmidt

Nils Matthes

Oliver Schlotterer

Bram Verbeek

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), Article 162. 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
Publicly Available Date	Oct 3, 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
Article Number	162
DOI	https://doi.org/10.1007/jhep12%282022%29162
Public URL	https://durham-repository.worktribe.com/output/1182352