Contributor info: Dr Ioannis Tsiares

Sylvain Ribault, Ioannis Tsiares

SciPost Phys. 17, 058 (2024) · published 22 August 2024 | Toggle abstract · pdf

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.