From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop

TL;DR

This paper explores the connection between open- and closed-string one-loop scattering amplitudes, revealing that modular graph functions in closed strings can be derived from open-string integrals via a generalized single-valued projection.

Contribution

It introduces a novel relationship between open- and closed-string amplitudes at one loop, extending the single-valued projection concept to higher genus.

Findings

Modular graph functions can be obtained from open-string integrals.

A generalized single-valued projection relates open- and closed-string amplitudes.

The approach provides insights into string dualities at one loop.

Abstract

We relate one-loop scattering amplitudes of massless open- and closed-string states at the level of their low-energy expansion. The modular graph functions resulting from integration over closed-string punctures are observed to follow from symmetrized open-string integrals through a tentative generalization of the single-valued projection known from genus zero.