FATEEV Vladimir
Fonction : Permanent
Emerite CNRS
(HDR)
Vladimir.FATEEV

umontpellier.fr
Bureau: 47, Etg: 1, Bât: 13 - Site : Campus Triolet
Domaines de Recherche: - Physique/Physique mathématique
- Physique/Physique des Hautes Energies - Théorie
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Dernieres productions scientifiques :

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Classical and quantum integrable sigma models. Ricci flow, "nice duality" and perturbed rational conformal field theories 
Auteur(s): Fateev V.
(Document sans référence bibliographique) 2019-02-07Texte intégral en Openaccess : 
Ref HAL: hal-02023484_v1
Ref Arxiv: 1902.02811
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: We consider classical and quantum integrable sigma models and their relations with the solutions of renormalization group equations. We say that an integrable sigma model possesses the "nice" duality property if the dual quantum field theory has the weak coupling region. As an example, we consider the deformed $CP(n-1)$ sigma model with additional quantum degrees of freedom. We formulate the dual integrable field theory and use perturbed conformal field theory, perturbation theory, $S$-matrix, Bethe Ansatz and renormalization group methods to show that this field theory has the "nice" duality property. We consider also an alternative approach to the analysis of sigma models on the deformed symmetric spaces, based on the perturbed rational conformal field theories.
Commentaires: 37 pages
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Integrability, Duality and Sigma Models 
Auteur(s): Fateev V., Litvinov Alexey V.
(Article) Publié:
Jhep, vol. 11 p.204 (2018)
Texte intégral en Openaccess : 
Ref HAL: hal-01774013_v1
Ref Arxiv: 1804.03399
Ref INSPIRE: 1667074
DOI: 10.1007/JHEP11(2018)204
WoS: 000453291500008
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
5 Citations
Résumé: We introduce and study conformal field theories specified by W −algebras commuting with certain set of screening charges. These CFT’s possess perturbations which define integrable QFT’s. We establish that these QFT’s have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the S−matrix of this QFT tends to the scattering matrix of the O(N) sigma model. The perturbation theory, Bethe ansatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFT’s are dual to integrable deformation of O(N) sigma-models.
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Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality 
Auteur(s): Fateev V.
(Article) Publié:
Sigma, vol. 13 p.080 (2017)
Texte intégral en Openaccess : 
Ref HAL: hal-01645538_v1
Ref Arxiv: 1705.06424
Ref INSPIRE: 1600255
DOI: 10.3842/SIGMA.2017.080
WoS: 000413172400001
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
5 Citations
Résumé: We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for different integrable perturbed conformal field theories. The perturbation theory, Bethe ansatz technique, renormalization group and methods of perturbed conformal field theory are applied to show that all integrable deformations of sine-Liouville model possess non-trivial duality properties.
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Integrable structure, W-symmetry and AGT relation 
Auteur(s): Fateev V., Litvinov A. V.
(Document sans référence bibliographique) 2011-11-15Texte intégral en Openaccess : 
Ref HAL: hal-00654717_v1
Ref Arxiv: 1109.4042
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: In these notes we consider integrable structure of the conformal field theory with the algebra of symmetries $\mathcal{A}=W_{n}\otimes H$, where $W_{n}$ is $W-$algebra and $H$ is Heisenberg algebra. We found the system of commuting Integrals of Motion with relatively simple properties. In particular, this system has very simple spectrum and the matrix elements of special primary operators between its eigenstates have nice factorized form coinciding exactly with the contribution of the bifundamental multiplet to the Nekrasov partition function for U(n) gauge theories.
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Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory 
Auteur(s): Bershtein M. A., Fateev V., Litvinov A. V.
(Article) Publié:
Nuclear Physics B, vol. 847 p.413-459 (2011)
Texte intégral en Openaccess : 
Ref HAL: hal-00654715_v1
DOI: 10.1016/j.nuclphysb.2011.01.035
WoS: 000290781400007
Exporter : BibTex | endNote
14 Citations
Résumé: In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic Liouville field theory described by three-exponential model. (C) 2011 Elsevier B.V. All rights reserved.
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