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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/2405.09325v3 (pdf) |
| Date submitted: | 2024-06-05 22:38 |
| 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 $c <1$. We also conjecture that the formulas have a well-defined limit as the central charge approaches rational values. 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.
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Current status:
In refereeing