Communications in Number Theory and Physics

Volume 10 (2016)

Number 4

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

Pages: 703 – 737



Federico Zerbini (Max Planck Institut für Mathematik, Bonn, Germany)


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.

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