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arXiv · 2310.09334

On the Virasoro fusion kernel at $c=25$

Sylvain Ribault·Ioannis Tsiares
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Abstract

We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlevé 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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Sylvain Ribault, Ioannis Tsiares. 2024-05-28. On the Virasoro fusion kernel at $c=25$. https://doi.org/10.21468/scipostphys.17.2.058

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