Superstring amplitudes and the associator

TL;DR

This paper reveals a pattern in superstring amplitudes' alpha' expansion linking multiple zeta values with the Drinfel'd associator, providing a new algebraic framework for understanding and computing these amplitudes.

Contribution

It establishes a novel connection between superstring amplitudes, motivic multiple zeta values, and the Drinfel'd associator, simplifying amplitude extraction.

Findings

Pattern correlates higher depth multiple zeta values with simple zeta values.

The relationship is explained via the coaction on motivic multiple zeta values.

The associator can be used to explicitly compute four-point amplitudes.

Abstract

We investigate a pattern in the $\alpha'$ expansion of tree-level open superstring amplitudes which correlates the appearance of higher depth multiple zeta values with that of simple zeta values in a particular way. We rephrase this relationship in terms of the coaction on motivic multiple zeta values and show that the pattern takes a very simple form, which can be simply explained by relating the amplitudes to the Drinfel'd associator derived from the Knizhnik-Zamolodchikov equation. Given this correspondence we show that, at least in the simplest case of the four-point amplitude, the associator can be used to extract the form of the amplitude.