All-order α'-expansion of one-loop open-string integrals

Authors: Carlos R. Mafra, Oliver Schlotterer

Preprint number: UUITP-34/19

We present a new method to evaluate the α'-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik–Zamolodchikov–Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp τ → i∞ and can be reduced to genus-zero integrals.