Periods and Superstring Amplitudes

Understand

Scattering amplitudes which describe the interaction of physical states play an important role in determining physical observables.

• In string theory the physical states are given by vibrations of open and closed strings and their interactions are described (at the leading order in perturbation theory) by a world-sheet given by the topology of a disk or sphere, respectively.
• Formally, for scattering of N strings this leads to N-3-dimensional iterated real integrals along the compactified real axis or N-3-dimensional complex sphere integrals, respectively.
• As a consequence the physical observables are described by periods on M_{0,N} - the moduli space of Riemann spheres of N ordered marked points.