Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2020-04

Johannes Broedel, André Kaderli, Oliver Schlotterer


Two dialects for KZB equations: generating one-loop open-string integrals.


Abstract: Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1,2]. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik–Zamolodchikov–Bernard(KZB) type on the twice-punctured torus.

We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2020-04


91 pp.