Abstract

It is well known that closed-string scattering at genus zero is related to open string scattering by the single-valued map of multiple zeta values (MZVs). In this sense, the so-called single-valued MZVs naturally occur in string theory. At higher genus an analogous connection between the open – and the closed string remains more tentative. In this talk, I will discuss recent work which aims to define such a mapping from open to closed strings at genus one, driven by the study of generating functions of string integrals. The low-energy expansions of the respective configuration-space integrals feature elliptic multiple zeta values for the open string and modular graph forms for the closed string. Paying particular attention to the resulting functions in the closed string context, I will discuss their connection to the single-valued and modular iterated Eisenstein integrals introduced in the mathematical literature. This connection indicates that said mapping defined for string scattering at genus one is again closely related to the concept of single-valuedness.   Co-authors: Jan Gerken (Chalmers U. Tech.), Axel Kleinschmidt (Max Planck Inst., Potsdam & Intl. Solvay Inst., Brussels), Carlos Mafra (Southampton U.), Oliver Schlotterer (Uppsala U.), Daniele Dorigoni (Durham U.), Mehregan Doroudiani (Max Planck Inst., Potsdam), Joshua Drewitt (Nottingham U.), Martijn Hidding (Uppsala U.), Nils Matthes (Copenhagen U.)