2019/06/30 by Eric D'Hoker, Michael B. Green · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.NT
paper · pdf · doi:10.1007/jhep07(2019)149
65 pages, 4 figures; typos corrected, reference added, minor edits in version 2; factor of 4 corrected in theorem 4.1 in version 3
arxiv created 2021/06/28 · arxiv updated 2021/06/29
It is well known that the low energy expansion of tree-level superstring scattering amplitudes satisfies a suitably defined version of maximum transcendentality. In this paper it is argued that there is a natural extension of this definition that applies to the genus-one four-graviton Type II superstring amplitude to all orders in the low-energy expansion. To obtain this result, the integral over the genus-one moduli space is partitioned into a region \cal MR surrounding the cusp and its complement \cal ML, and an exact expression is obtained for the contribution to the amplitude from \cal MR. The low-energy expansion of the \cal MR contribution is proven to be free of irreducible multiple zeta-values to all orders. The contribution to the amplitude from \cal ML is computed in terms of modular graph functions up to order D12 \cal R4 in the low-energy expansion, and general arguments are used beyond this order to conjecture the transcendentality properties of the \cal ML contributions. Maximal transcendentality of the full amplitude holds provided we assign a non-zero weight to certain harmonic sums, an assumption which is familiar from transcendentality assignments in quantum field theory amplitudes.