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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 2, Pages 232–262
DOI: https://doi.org/10.4213/tmf9141 (Mi tmf9141) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Free fermions, $W$-algebras, and isomonodromic deformations

P. G. Gavrilenkoab, A. V. Marshakovcdb

a Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
b Department of Mathematics, National Research University Higher School of Economics, Moscow, Russia
c Lebedev Physical Institute, RAS, Moscow, Russia
d Institute for Theoretical and Experimental Physics, Moscow, Russia
Full-text PDF (708 kB) Citations (17)
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DOI: https://doi.org/10.4213/tmf9141
Abstract: We consider the theory of multicomponent free massless fermions in two dimensions and use it to construct representations of $W$-algebras at integer Virasoro central charges. We define the vertex operators in this theory in terms of solutions of the corresponding isomonodromy problem. We use this construction to obtain some new insights into tau functions of the multicomponent Toda-type hierarchies for the class of solutions given by the isomonodromy vertex operators and to obtain a useful representation for tau functions of isomonodromic deformations.
Keywords: two-dimensional conformal field theory, $W$-algebra, isomonodromic deformation.
Funding agency Grant number
Russian Foundation for Basic Research 01-01-14
14-01-90405
15-01-99504
Centre National de la Recherche Scientifique F14-2015
Japan Society for the Promotion of Science 15-51-50034
Ministry of Education and Science of the Russian Federation НШ-1500.2014.2
This paper was prepared within the framework of a subsidy granted to the National Research University Higher School of Economics by the Government of the Russian Federation for the implementation of the Global Competitiveness Program. The research of P. G. Gavrylenko was supported by a joint Ukrainian–Russian project (NASU-RFBR Project No. 01-01-14), a joint NASU-CNRS project (Project No. F14-2015), and a “Young Russian Mathematics” stipend. The research of A. V. Marshakov was supported by a joint Ukrainian–Russian project (NASU-RFBR Project No. 14-01-90405), the Russian Foundation for Basic Research (Grant No.-15-01-99504), a joint RFBR/JSPS project (Project No. 15-51-50034), and the Program for Supporting Leading Scientific Schools (Grant No. NSh-1500.2014.2).
Received: 10.01.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 2, Pages 649–677
DOI: https://doi.org/10.1134/S0040577916050044
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. G. Gavrilenko, A. V. Marshakov, “Free fermions, $W$-algebras, and isomonodromic deformations”, TMF, 187:2 (2016), 232–262; Theoret. and Math. Phys., 187:2 (2016), 649–677
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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