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

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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

$W$ -algebras, and isomonodromic deformations

P. G. Gavrilenko^ab, A. V. Marshakov^cdb

^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

$W$ -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

$W$ -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

$W$ -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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Linking options:

https://www.mathnet.ru/eng/tmf9141

https://doi.org/10.4213/tmf9141

https://www.mathnet.ru/eng/tmf/v187/i2/p232

This publication is cited in the following 17 articles:

Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko, “Isomonodromic Tau Functions on a Torus as Fredholm Determinants, and Charged Partitions”, Commun. Math. Phys., 398:3 (2023), 1029
Ioana Coman, Elli Pomoni, Jörg Teschner, “From Quantum Curves to Topological String Partition Functions”, Commun. Math. Phys., 399:3 (2023), 1501
M. Semenyakin, “Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux”, J. High Energ. Phys., 2022:10 (2022)
Bruno Le Floch, “A slow review of the AGT correspondence”, J. Phys. A: Math. Theor., 55:35 (2022), 353002
Mikhail Bershtein, Pavlo Gavrylenko, Alba Grassi, “Quantum Spectral Problems and Isomonodromic Deformations”, Commun. Math. Phys., 393:1 (2022), 347
M. Bertola, Fabrizio Del Monte, J. Harnad, “Fredholm Pfaffian $\tau$ -Functions for Orthogonal Isospectral and Isomonodromic Systems”, Ann. Henri Poincaré, 23:12 (2022), 4521
G. Bonelli, F. Del Monte, P. Gavrylenko, A. Tanzini, “Circular quiver gauge theories, isomonodromic deformations and W-N fermions on the torus”, Lett. Math. Phys., 111:3 (2021), 83
Mikhail Bershtein, Roman Gonin, “Twisted Representations of Algebra of $q$ -Difference Operators, Twisted $q$ - $W$ Algebras and Conformal Blocks”, SIGMA, 16 (2020), 077, 55 pp.
P. Gavrylenko, N. Iorgov, O. Lisovyy, “Higher-rank isomonodromic deformations and w-algebras”, Lett. Math. Phys., 110:2 (2020), 327–364
Bonelli G., Del Monte F., Gavrylenko P., Tanzini A., “N=2Gauge Theory, Free Fermions on the Torus and Painleve Vi”, Commun. Math. Phys., 377:2 (2020), 1381–1419
M. Bershtein, A. Shchechkin, “Painleve equations from nakajima-yoshioka blowup relations”, Lett. Math. Phys., 109:11 (2019), 2359–2402
G. Bonelli, A. Grassi, A. Tanzini, “New results in $\mathcal N=2$ theories from non-perturbative string”, Ann. Henri Poincare, 19:3 (2018), 743–774
P. Gavrylenko, O. Lisovyy, “Pure $\mathrm{SU(2)}$ gauge theory partition function and generalized Bessel kernel”, String-Math 2016, Proceedings of Symposia in Pure Mathematics, 98, eds. A. Kashani-Poor, R. Minasian, N. Nekrasov, B. Pioline, Amer. Math. Soc., 2018, 181–205
P. Gavrylenko, O. Lisovyy, “Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions”, Commun. Math. Phys., 363:1 (2018), 1–58
M. Bershtein, P. Gavrylenko, A. Marshakov, “Twist-field representations of W-algebras, exact conformal blocks and character identities”, J. High Energy Phys., 2018, no. 8, 108
A. R. Its, O. Lisovyy, A. Prokhorov, “Monodromy dependence and connection formulae for isomonodromic tau functions”, Duke Math. J., 167:7 (2018)
G. Bonelli, O. Lisovyy, K. Maruyoshi, A. Sciarappa, A. Tanzini, “On Painlevé/gauge theory correspondence”, Lett. Math. Phys., 107:12 (2017), 2359–2413

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