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(35) Production(s) de FATEEV V.
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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:
Journal Of High Energy Physics, 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
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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
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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
Ref Arxiv: 1011.4090
DOI: 10.1016/j.nuclphysb.2011.01.035
WoS: 000290781400007
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
15 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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On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture
Auteur(s): Alba Vasyl A., Fateev V., Litvinov Alexey V., Tarnopolskiy Grigory M.
(Article) Publié:
Letters In Mathematical Physics, vol. 98 p.33-64 (2011)
Texte intégral en Openaccess :
Ref HAL: hal-00654713_v1
Ref Arxiv: 1012.1312
DOI: 10.1007/s11005-011-0503-z
WoS: 000294964200002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
162 Citations
Résumé: In their recent paper, Alday et al. (Lett Math Phys 91: 167-197, 2010) proposed a relation between N = 2 four-dimensional supersymmetric gauge theories and twodimensional conformal field theories. As part of their conjecture they gave an explicit combinatorial formula for the expansion of the conformal blocks inspired by the exact form of the instanton part of the Nekrasov partition function. In this paper we study the origin of such an expansion from a CFT point of view. We consider the algebra A= Vir circle times H which is the tensor product of mutually commuting Virasoro and Heisenberg algebras and discover the special orthogonal basis of states in the highest weight representations of A. The matrix elements of primary fields in this basis have a very simple factorized form and coincide with the function called Z(bif) appearing in the instanton counting literature. Having such a simple basis, the problem of computation of the conformal blocks simplifies drastically and can be shown to lead to the expansion proposed in Alday et al. (2010). We found that this basis diagonalizes an infinite system of commuting Integrals of Motion related to Benjamin-Ono integrable hierarchy.
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The large central charge limit of conformal blocks
Auteur(s): Fateev V., Ribault S.
(Article) Publié:
Journal Of High Energy Physics, vol. p.JHEP02(2012)001 (2012)
Texte intégral en Openaccess :
Ref HAL: hal-00627906_v3
Ref Arxiv: 1109.6764
DOI: 10.1007/JHEP02(2012)001
WoS: 000301451200001
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
22 Citations
Résumé: We study conformal blocks of conformal field theories with a W3 symmetry algebra in the limit where the central charge is large. In this limit, we compute the four-point block as a special case of an sl3-invariant function. In the case when two of the four fields are semi-degenerate, we check that our results agree with the block's combinatorial expansion as a sum over Young diagrams. We also show that such a block obeys a sixth-order differential equation, and that it has an unexpected singularity at z=-1, in addition to the expected singularities at z=0,1,infinity.
Commentaires: 22 pages, v3: added clarifications and references in Section 2, other minor improvements, published in JHEP.
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