Single-valued multiple zeta values in genus $1$ superstring amplitudes

We study the functions $D_{\underline{l}}$ introduced by Green, Russo, Vanhove in “Low energy expansion of the four-particle genus-one amplitude in type II superstring theory” [JHEP (2008), no. 0802] in the context of type II superstring scattering amplitudes of $4$ gravitons on a torus. In particular we describe a method to algorithmically compute the coefficients in their expansion at the cusp in terms of conical sums. We perform explicit computations for $3$-graviton functions, which naturally suggest to conjecture that only single-valued multiple zeta values appear.

Full Text (PDF format)

Published 3 April 2017