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arXiv · 2007.03712

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

Johannes Broedel·André Kaderli·Oliver Schlotterer
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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.

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Johannes Broedel, André Kaderli, Oliver Schlotterer. 2020-07-07. Two dialects for KZB equations: generating one-loop open-string integrals. https://doi.org/10.1007/jhep12(2020)036

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