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Pré-Publication, Document De Travail Année : 2023

On the Virasoro fusion kernel at $c=25$

Résumé

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.

Dates et versions

hal-04265743 , version 1 (31-10-2023)

Identifiants

Citer

Sylvain Ribault, Ioannis Tsiares. On the Virasoro fusion kernel at $c=25$. 2023. ⟨hal-04265743⟩
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