Contributor info: Dr Julien Roussillon

Julien Roussillon

SciPost Phys. 17, 138 (2024) · published 20 November 2024 | Toggle abstract · pdf

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.