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On the Virasoro fusion and modular kernels at any irrational central charge
by Julien Roussillon
Submission summary
| Authors (as registered SciPost users): | Julien Roussillon |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.09325v4 (pdf) |
| Date submitted: | 2024-10-10 08:20 |
| Submitted by: | Roussillon, Julien |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and $c <1$. Our proposal for $c <1$ agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for $c\in \mathbb C \backslash (-\infty,1]$ agrees numerically with Ponsot and Teschner's integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
I modified the manuscript according to the recommendations of the referees. The list of changes can be found in the detailed answered to the referees' comments.
Current status:
Reports on this Submission
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The author has satisfactorily addressed my comments and questions on the previous version of their draft and I am now happy to recommend this paper for publication in SciPost.
Recommendation
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Report #1 by Sylvain Ribault (Referee 1) on 2024-10-10 (Invited Report)
Report
The author has taken my remarks into account, and carefully answered my questions. The article's new version is significantly improved, both in form and in substance. I have no further improvements to suggest.
NB: As a matter of principle, I have no recommendation about publication in this or that journal. Since it is necessary to select a recommendation for submitting a report, I picked the first one in the list.
Recommendation
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