On the Virasoro fusion and modular kernels at any irrational central charge
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∈ C (-∞,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∈ C (-∞,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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