Abstract:
We study the fusion kernel for nondegenerate conformal blocks in the Liouville theory as a solution of difference equations originating from the pentagon identity. We propose an approach for solving these equations based on a "nonperturbative" series expansion that allows calculating the fusion kernel iteratively. We also find exact solutions for the special central charge values $c=1+6(b-b^{-1})^2$, $b\in\mathbb N$. For $c=1$, the obtained result reproduces the formula previously obtained from analytic properties of a solution of a Painlevé equation, but our solution has a significantly simplified form.
Keywords:conformal field theory, Liouville theory, Virasoro algebra.
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