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arXiv · 2511.15240

A construction of single-valued elliptic polylogarithms

Konstantin Baune·Johannes Broedel·Yannis Moeckli
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Abstract

We establish a general construction of single-valued elliptic polylogarithms as functions on the once-punctured elliptic curve. Our formalism is an extension of Brown's construction of genus-zero single-valued polylogarithms to the elliptic curve: the condition of trivial monodromy for solutions to the Knizhnik-Zamolodchikov-Bernard equation is expressed in terms of elliptic associators and involves two representations of a two-letter alphabet. Our elliptic single-valued condition reduces to Brown's genus-zero condition upon degeneration of the torus. We provide several examples for our construction, including the elliptic Bloch-Wigner dilogarithm.

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Konstantin Baune, Johannes Broedel, Yannis Moeckli. 2025-11-19. A construction of single-valued elliptic polylogarithms. https://doi.org/10.21468/scipostphys.21.1.006

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