SciPost Submission Page
A construction of single-valued elliptic polylogarithms
by Konstantin Baune, Johannes Broedel, Yannis Moeckli
Submission summary
| Authors (as registered SciPost users): | Konstantin Baune |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2511.15240v1 (pdf) |
| Date submitted: | Dec. 5, 2025, 1:39 p.m. |
| Submitted by: | Konstantin Baune |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing