Generating series of all modular graph forms from iterated Eisenstein integrals

Understand

We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes.

• By analysing the differential equation of the generating series we construct a solution for its low-energy expansion to all orders in the inverse string tension $\alpha'$.
• Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus.
• These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of real-analytic modular forms.