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Presque toutes les Théories de Champs Quantiques en dimension deux peuvent être considérées comme Théories de Champs Conformes perturbées. On montre que les méthodes de calcul pour les valeurs moyennes dans le vide et le développement à courte distance, combinés avec le bootstrap des facteurs de forme dans les théories intégrables permettent de calculer les fonctions de corrélation à deux points avec grande précision.

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La méthode de l'Intégral de Coulomb, basée sur la représentation du champs libre, est une méthode puissante pour l'analyse de fonctions de corrélation en Théories de Champs Conformes. On utilise cette méthode au calcul de certaines fonctions à trois et quatre points dans la théorie de Liouville et dans celle de Toda.

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DOI: 10.1088/0305-4470/39/41/S10
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17 Citations
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We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is terminated at a nontrivial infrared fixed point. We identify a form of whole boundary state corresponding to this fixed point.

Commentaires: 54 pages

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Ref Arxiv: hep-th/0505120
DOI: 10.1134/1.2029952
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32 Citations
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The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in contrast to the Liouville Field Theory. Some additional assumptions for other fields are required. Under these assumptions we write such a differential equation and solve it explicitly. We use the fusion properties of the operator algebra to derive a special set of three-point correlation function. The result agrees with the semiclassical calculations.

Commentaires: 5 pages - voir aussi Pisma Zh.Eksp.Teor.Fiz. 81 (2005) 728-732

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Ref Arxiv: math-ph/0407021
DOI: 10.1088/0305-4470/37/47/007
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A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; thses can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.

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Ref Arxiv: hep-th/0402082
DOI: 10.1016/j.nuclphysb.2004.06.043
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7 Citations
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A two-parametric family of integrable models (the SS model) that contains as particular cases several well known integrable quantum Field theories is considered. After the quantum group restrictionit describes a wide class of integrable perturbed conformal field theories. Exponential Fields in the SS model are closely related to the primary fields in these perturbed theories. We use the bosonization approach to derive an integral representation for the form factors of the exponential fields in the SS model. The same representations for the sausage model and the cosine-cosine model are obtained as limiting cases. The results are tested at the special points, where the theory contains free particles.

Commentaires: 37 pages, 3 figures; some misprints corrected; Eq. (B.12b) corrected

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Ref Arxiv: math-ph/0307010
DOI: 10.1088/0305-4470/36/47/014
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5 Citations
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An eigenvalue problem relevant for the non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime (large R) the eigenvalues admit a power series expansion around the IR critical point R → ∞. We compute high order coefficients and prove that the series converges for all finite values of R. In the ultraviolet (UV) limit the spectrum condenses into a continuum spectrum with a set of residual bound states. The spectrum agrees nicely with the central charge computed by the thermodynamic Bethe ansatz method.