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arXiv · 2405.09325

On the Virasoro fusion and modular kernels at any irrational central charge

Julien Roussillon
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Abstract

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 $c\in \mathbb C \backslash (-\infty,1]$ 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 $c\in \mathbb C \backslash (-\infty,1]$ 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.

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Julien Roussillon. 2024-05-15. On the Virasoro fusion and modular kernels at any irrational central charge. https://doi.org/10.21468/scipostphys.17.5.138

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