Polylogarithms, multiple zeta values and superstring amplitudes

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. A formalism is provided to calculate tree amplitudes in open superstring theory for any multiplicity at any order in the inverse string tension. In particular, the world-sheet integrands of open-string tree amplitudes are closely related to the Kawai-Lewellen-Tye representation of supergravity amplitudes. This helps to reduce the singular parts of world-sheet disk integrals - including their string corrections - to lower-point results. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.