From modular graph forms to iterated integrals

Abstract

Abstract Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of modular graph forms into iterated integrals of holomorphic Eisenstein series and provide a Mathematica package that implements all modular graph form topologies up to four vertices. To achieve this, we introduce specific tree-representations of modular graph forms. The presented method enables the conversion of the integrand of the four-graviton one-loop amplitude in Type II superstring theory at eighth order in the inverse string tension α ′8, which we use to calculate the α ′8 ζ 3 ζ 5 contribution to the analytic part of the amplitude.

Keywords

• Scattering Amplitudes
• Superstrings and Heterotic Strings