Single-valued multiple zeta values in genus 1 superstring amplitudes

TL;DR

This paper investigates modular graph functions in genus 1 superstring amplitudes, providing an algorithmic method to compute their expansions and suggesting that only single-valued multiple zeta values appear in these expansions.

Contribution

It introduces a new algorithmic approach to compute coefficients of modular graph functions and conjectures the exclusive appearance of single-valued multiple zeta values in their expansions.

Findings

Explicit computations for 3-graviton functions.

Conjecture that only single-valued multiple zeta values appear.

Method to compute expansion coefficients at the cusp.

Abstract

We study the modular graph functions introduced by Green, Russo, Vanhove in the context of type II superstring scattering amplitudes of 4 gravitons on a torus. In particular we describe a method to algorithmically compute the coefficients in their expansion at the cusp in terms of conical sums. We perform explicit computations for 3-graviton functions, which naturally suggest to conjecture that only single-valued multiple zeta values appear.