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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 2, Pages 198–218
DOI: https://doi.org/10.4213/tmf9137 (Mi tmf9137) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Fusion transformations in Liouville theory

N. A. Nemkovab

a State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
Full-text PDF (549 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf9137
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-1500.2014.2
Russian Foundation for Basic Research 13-02-00457
14-02-31372-мол_а
This research is supported in part by the Program for Supporting Leading Scientific Schools (Grant No. NSh-1500.2014.2) and the Russian Foundation for Basic Research (Grant Nos. 13-02-00457 and 14-02-31372-mol_a).
Received: 09.11.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 2, Pages 1574–1591
DOI: https://doi.org/10.1134/S0040577916110040
Bibliographic databases:
PACS: 11.25.Hf
MSC: 17B68, 81R10
Language: Russian
Citation: N. A. Nemkov, “Fusion transformations in Liouville theory”, TMF, 189:2 (2016), 198–218; Theoret. and Math. Phys., 189:2 (2016), 1574–1591
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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