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On the Virasoro fusion and modular kernels at any irrational central charge
by Julien Roussillon
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Submission summary
| Authors (as registered SciPost users): | Julien Roussillon |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.09325v4 (pdf) |
| Date accepted: | 2024-10-29 |
| 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
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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.
Published as SciPost Phys. 17, 138 (2024)
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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