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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 6 scientific papers (total in 6 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 (6)
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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)2c=1+6(b−b−1)2, b∈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 6 articles:
    1. Julien Roussillon, “On the Virasoro fusion and modular kernels at any irrational central charge”, SciPost Phys., 17:5 (2024)  crossref
    2. Bruno Le Floch, “A slow review of the AGT correspondence”, J. Phys. A: Math. Theor., 55:35 (2022), 353002  crossref
    3. J. Roussillon, “The Virasoro fusion kernel and Ruijsenaars' hypergeometric function”, Lett. Math. Phys., 111:1 (2021), 7  crossref  mathscinet  isi
    4. Ch.-Ts. Chan, A. Mironov, A. Morozov, A. Sleptsov, “Orthogonal polynomials in mathematical physics”, Rev. Math. Phys., 30:6, SI (2018), 1840005, 64 pp.  crossref  mathscinet  zmath  isi  scopus
    5. Andrei Mironov, Alexei Morozov, “Check-Operators and Quantum Spectral Curves”, SIGMA, 13 (2017), 047, 17 pp.  mathnet  crossref
    6. N. Nemkov, “Analytic properties of the Virasoro modular kernel”, Eur. Phys. J. C, 77:6 (2017), 368  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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