All orderα′-expansion of superstring trees from the Drinfeld associator

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.