Elliptic multiple zeta values and one-loop superstring amplitudes

TL;DR

This paper explores elliptic multiple zeta values, a genus-one generalization of multiple polylogarithms, and applies them to compute one-loop superstring scattering amplitudes, enabling automated calculations of low energy limits.

Contribution

It introduces elliptic multiple zeta values as a natural framework for one-loop superstring amplitudes, extending existing polylogarithm techniques to genus-one cases.

Findings

Elliptic multiple zeta values generalize multiple zeta values to elliptic curves.

The formalism allows for automated calculation of one-loop superstring amplitudes.

The approach simplifies expressing low energy limits of superstring scattering processes.

Abstract

We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.