Modular graph forms from equivariant iterated Eisenstein integrals

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

Preprint number: UUITP-37/22

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms dubbed "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.

FOLLOW UPPSALA UNIVERSITY ON

Uppsala University on Facebook
Uppsala University on Instagram
Uppsala University on Youtube
Uppsala University on Linkedin