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On the Virasoro fusion kernel at $c=25$
by Sylvain Ribault, Ioannis Tsiares
Submission summary
| Authors (as registered SciPost users): | Sylvain Ribault · Ioannis Tsiares |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2310.09334v2 (pdf) |
| Date submitted: | 2024-06-03 09:57 |
| Submitted by: | Tsiares, Ioannis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlev\'e VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The derivation of our formula relies on a duality $c\to 26-c$ that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for $c<1$ the fusion and modular kernels are not smooth functions, but distributions.
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Current status:
In refereeing