A construction of single-valued elliptic polylogarithms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916021951004672 |
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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 |