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Genus-zero and genus-one string amplitudes and special multiple zeta values

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Zagier,  Don
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Zagier, D., & Zerbini, F. (2020). Genus-zero and genus-one string amplitudes and special multiple zeta values. Communications in Number Theory and Physics, 14(2), 413-452. doi:10.4310/CNTP.2020.v14.n2.a4.


Cite as: https://hdl.handle.net/21.11116/0000-0006-BC4E-0
Abstract
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 Broedel, Schlotterer and the second author.