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

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Kaderli,  André
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Broedel, J., Kaderli, A., & Schlotterer, O. (2020). Two dialects for KZB equations: generating one-loop open-string integrals. Journal of High Energy Physics, 2020(12): 36. doi:10.1007/JHEP12(2020)036.


Cite as: http://hdl.handle.net/21.11116/0000-0006-C612-6
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 \rcites{Mafra:2019xms, *Mafra:2019ddf, Broedel:2019gba}. 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.