On the Virasoro fusion kernel at $c=25$
High Energy Physics - Theory
2024-08-21 v2 Mathematical Physics
math.MP
Abstract
We find a formula for the Virasoro fusion kernel at , 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 that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for the fusion and modular kernels are not smooth functions, but distributions.
Cite
@article{arxiv.2310.09334,
title = {On the Virasoro fusion kernel at $c=25$},
author = {Sylvain Ribault and Ioannis Tsiares},
journal= {arXiv preprint arXiv:2310.09334},
year = {2024}
}
Comments
18 pages, plus an ancillary Python notebook -- v2: clarified a few points, discussed the series representation