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Higher-genus Fay-like identities from meromorphic generating functions
by Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Konstantin Baune · Egor Im |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202501_00030v1 (pdf) |
| Date accepted: | 2025-02-18 |
| Date submitted: | 2025-01-15 17:34 |
| Submitted by: | Baune, Konstantin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations between polylogarithms rely on identities for those integration kernels. In this article, we derive identities for Enriquez' meromorphic generating function and investigate the implications for the associated integration kernels. The resulting identities are shown to be exhaustive and therefore reproduce all identities for Enriquez' kernels conjectured in arXiv:2407.11476 recently.
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
Author comments upon resubmission
A detailed list of changes can be found below. See also the direct replies to the reports of the referees.
List of changes
- Definition 1 changed to Proposition. Sentence added in the paragraph below, explaining that for the purpose of the current article it is sufficient to consider the connection K(z, x) as a formal mathematical object, whereas an explicit realization is provided in ref. [31].
- Sentence added after eqn. (2.3) explaining the particular order of algebra elements appearing in eqn. (2.3)
- Footnote added on page 10 (footnote 8) describing the formal meaning of the appearance of inverse algebra elements in eqn. (3.8) and linking to the corresponding formula in the appendix
- Changed "between" to "among" where appropriate
- Deleting the word "transform" in the paragraph below eqn. (7.7)
- Paragraph added below eqn. (7.17) pointing out the features of our numerical evaluation and giving a new reference (ref. [31]) for the code package to be published in the future
Published as SciPost Phys. 18, 093 (2025)
Reports on this Submission
Report
In this new version the authors have added comments on the numerical evaluation of multiple polylogarithms on higher-genus Riemann surfaces. With this, the interested reader either knows that such software is currently being developed, and if they really want, they can contact the person developing it.
With this, I feel the authors have satisfied my previous request, and I'm happy to recommend publication of this work.
Requested changes
None
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)