A construction of single-valued elliptic polylogarithms

Fuente: arXiv
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Auteurs principaux: Baune, Konstantin, Broedel, Johannes, Moeckli, Yannis
Format: Preprint
Publié: 2025
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author Baune, Konstantin
Broedel, Johannes
Moeckli, Yannis
author_facet Baune, Konstantin
Broedel, Johannes
Moeckli, Yannis
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15240
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A construction of single-valued elliptic polylogarithms
Baune, Konstantin
Broedel, Johannes
Moeckli, Yannis
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Number Theory
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.
title A construction of single-valued elliptic polylogarithms
topic High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Number Theory
url https://arxiv.org/abs/2511.15240