TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.058
TI  - On the Virasoro fusion kernel at $c=25$
PY  - 2024/08/22
UR  - https://scipost.org/SciPostPhys.17.2.058
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 058
A1  - Ribault, Sylvain
AU  - Tsiares, Ioannis
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.2.058,
	title={{On the Virasoro fusion kernel at $c=25$}},
	author={Sylvain Ribault and Ioannis Tsiares},
	journal={SciPost Phys.},
	volume={17},
	pages={058},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.058},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.058},
}