Geodesic
Fusion transformations in Liouville theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 198-218 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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N. A. Nemkov. Fusion transformations in Liouville theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 198-218. http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a3/

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