The Structure of n-Point One-Loop Open Superstring Amplitudes

Understand

In this article we present the worldsheet integrand for one-loop amplitudes in maximally supersymmetric superstring theory involving any number n of massless open string states.

• The polarization dependence is organized into the same BRST invariant kinematic combinations which also govern the leading string correction to tree level amplitudes.
• The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S_3^{n-1} of first kind.
• We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang Mills theory and on the other hand the color tensors at quadratic alpha prime order of the color dressed tree amplitude.