On fusion kernel in Liouville theory

Abstract

We study fusion kernel for non-degenerate conformal blocks in Liouville theory as a solution to the difference equations originating from the pentagon identity. We suggest an approach to these equations based on 'non-perturbative' series expansion which allows to calculate the fusion kernel iteratively. We also find the exact solutions for the cases when the central charge is $c=1+6(b-b^{-1}{)}^2$ and $b\in \mathbb{N}$. For $c=1$ our result reproduces the formula, obtained earlier from analytical continuation via Painlevé equation. However, in our case it appears in a significantly simplified form.

23 pages, version 2 with minor corrections added

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Cited by in corpus (6)

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• Check-Operators and Quantum Spectral Curves
• Analytic properties of the Virasoro modular kernel
• On new exact conformal blocks and Nekrasov functions