Motivic Multiple Zeta Values and Superstring Amplitudes

TL;DR

This paper explores the structure of superstring amplitudes, revealing a decomposition involving motivic multiple zeta values and a Hopf algebra framework, leading to simplified and elegant representations of these amplitudes.

Contribution

It introduces a novel decomposition of superstring amplitudes using motivic multiple zeta values and a Hopf algebra morphism, providing a new algebraic perspective.

Findings

Decomposition of open superstring amplitude into multiple zeta value classes

Mapping of alpha'-expansion onto a non-commutative Hopf algebra

Simplified and symmetric form of superstring amplitudes

Abstract

The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows to disentangle its alpha'-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the alpha'-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the alpha'-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the alpha'-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form.