Polylogarithms, Multiple Zeta Values and Superstring Amplitudes

TL;DR

This paper introduces a formalism for calculating open superstring tree amplitudes at any multiplicity and order, revealing deep connections with Yang-Mills and supergravity amplitudes through polylogarithm techniques.

Contribution

It establishes a novel formalism linking superstring amplitudes with field theory amplitudes and systematically addresses their singular and regular parts using polylogarithms.

Findings

Unified approach to superstring and field theory amplitudes

Reduction of complex integrals to lower-point results

Systematic handling of regular parts with polylogarithms

Abstract

A formalism is provided to calculate tree amplitudes in open superstring theory for any multiplicity at any order in the inverse string tension. We point out that the underlying world-sheet disk integrals share substantial properties with color-ordered tree amplitudes in Yang-Mills field theories. In particular, we closely relate world-sheet integrands of open-string tree amplitudes to the Kawai-Lewellen-Tye representation of supergravity amplitudes. This correspondence helps to reduce the singular parts of world-sheet disk integrals -including their string corrections- to lower-point results. The remaining regular parts are systematically addressed by polylogarithm manipulations.