Single-valued integration and superstring amplitudes in genus zero

Understand

We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper.

• Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp.
• single-valued multiple zeta values).
• Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion.