All order alpha'-expansion of superstring trees from the Drinfeld associator

TL;DR

This paper derives a recursive formula for superstring tree amplitudes' alpha'-expansion, revealing that string corrections to Yang-Mills theory are governed by the Drinfeld associator, applicable across various dimensions and supersymmetries.

Contribution

It introduces a novel recursive approach to compute superstring amplitude expansions involving the Drinfeld associator, unifying string corrections across different theories.

Findings

Recursive formula for alpha'-expansion derived

String corrections linked to Drinfeld associator

Applicable to any number of dimensions and supersymmetries

Abstract

We derive a recursive formula for the alpha'-expansion of superstring tree amplitudes involving any number N of massless open string states. String corrections to Yang-Mills field theory are shown to enter through the Drinfeld associator, a generating series for multiple zeta values. Our results apply for any number of spacetime dimensions or supersymmetries and chosen helicity configurations.