TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.5.138
TI  - On the Virasoro fusion and modular kernels at any irrational central charge
PY  - 2024/11/20
UR  - https://scipost.org/SciPostPhys.17.5.138
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 5
SP  - 138
A1  - Roussillon, Julien
AB  - We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases $c∈ \mathbb{C} \backslash (-∞,1]$ and $c <1$. Our proposal for $c <1$ agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for $c∈ \mathbb{C} \backslash (-∞,1]$ agrees numerically with Ponsot and Teschner's integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.
ER  -

@Article{10.21468/SciPostPhys.17.5.138,
	title={{On the Virasoro fusion and modular kernels at any irrational central charge}},
	author={Julien Roussillon},
	journal={SciPost Phys.},
	volume={17},
	pages={138},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.5.138},
	url={https://scipost.org/10.21468/SciPostPhys.17.5.138},
}