The Number Theory of Superstring Amplitudes

Abstract

The following article is intended as a survey of recent results at the interface of number theory and superstring theory. We review the expansion of scattering amplitudes—central observables in field and string theory—in the inverse string tension where elegant patterns of multiple zeta values occur. More specifically, the Drinfeld associator and the Hopf algebra structure of motivic multiple zeta values are shown to govern tree-level amplitudes of the open superstring. Partial results on the quantum corrections are discussed where elliptic analogues of multiple zeta values play a central rle.