Communications in Number Theory and Physics
Volume 14 (2020)
Genus-zero and genus-one string amplitudes and special multiple zeta values
Pages: 413 – 452
In this paper we show that in perturbative string theory the genus-one contribution to formal $2$‑point amplitudes can be related to the genus-zero contribution to $4$‑point amplitudes. This is achieved by studying special linear combinations of multiple zeta values that appear as coefficients of the amplitudes. We also exploit our results to relate closed strings to open strings at genus one using Brown’s single-valued projection, proving a conjecture of J. Broedel, O. Schlotterer, and F. Zerbini .
Received 21 July 2019
Accepted 17 December 2019
Published 30 March 2020