Ref HAL: hal-00498565_v2
DOI: 10.1007/JHEP12(2010)089
WoS: 000285964200003
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12 Citations
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We investigate sl(n) conformal Toda theory with maximally symmetric boundaries. There are two types of maximally symmetric boundary conditions, due to the existence of an order two automorphism of the W-n >= 3 algebra. In one of the two cases, we find that there exist D-branes of all possible dimensions 0 <= d <= n - 1, which correspond to partly degenerate representations of the W-n algebra. We perform classical and conformal bootstrap analyses of such D-branes, and relate these two approaches by using the semi-classical light asymptotic limit. In particular we determine the bulk one-point functions. We observe remarkably severe divergences in the annulus partition functions, and attribute their origin to the existence of infinite multiplicities in the fusion of representations of the W-n >= 3 algebra. We also comment on the issue of the existence of a boundary action, using the calculus of constrained functional forms, and derive the generating function of the Backlund transformation for sl(3) Toda classical mechanics, using the minisuperspace limit of the bulk one-point function.

Commentaires: 42 pages, version 2: reference [20] added, other small improvements made, published in JHEP

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Ref Arxiv: 0912.0504
DOI: 10.1007/JHEP02(2010)014
WoS: 000275223100014
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92 Citations
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In these notes we consider relation between conformal blocks and the Nekrasov partition function of certain $\mathcal{N}=2$ SYM theories proposed recently by Alday, Gaiotto and Tachikawa. We concentrate on $\mathcal{N}=2^{*}$ theory, which is the simplest example of AGT relation.

Ref HAL: hal-00423713_v1
Ref Arxiv: 0909.3347
DOI: 10.1088/1751-8113/42/30/304013
WoS: 000267943000014
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8 Citations
Résumé:

We study correlation functions of parafermionic currents and disorder fieldsin the Z(N) symmetric conformal field theory perturbed by the first thermaloperator. Following the ideas of Al. Zamolodchikov, we develop for thecorrelation functions the conformal perturbation theory at small scales and theform factors spectral decomposition at large ones. For all N there is anagreement between the data at the intermediate distances. We consider theproblems arising in the description of the space of scaling fields in perturbedmodels, such as null vector relations, equations of motion and a consistenttreatment of fields related by a resonance condition.

Commentaires: 29 pp

Ref HAL: hal-00423711_v1
DOI: 10.1088/1751-8113/42/30/304012
WoS: 000267943000013
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13 Citations
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We study 't Hooft's integral equation determining the meson masses M_n in multicolor QCD_2. In this note we concentrate on developing an analytic method, and restrict our attention to the special case of quark masses m_1=m_2=g/\sqrt{\pi}. Among our results is systematic large-n expansion, and exact sum rules for M_n. Although we explicitly discuss only the special case, the method applies to the general case of the quark masses, and we announce some preliminary results for m_1=m_2.

Ref HAL: hal-00379184_v1
Ref Arxiv: 0902.1331
DOI: 10.1088/1751-8113/42/30/304011
WoS: 000267943000012
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41 Citations
Résumé:

Liouville field theory on a sphere is considered. We explicitly derive adifferential equation for four-point correlation functions with one degeneratefield $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-pointconformal blocks which can be calculated exactly and represented by finitedimensional integrals of elliptic theta-functions for arbitrary intermediatedimension. We study also the bootstrap equations for these conformal blocks andderive integral representations for corresponding four-point correlationfunctions. A relation between the one-point correlation function of a primaryfield on a torus and a special four-point correlation function on a sphere isproposed.

Commentaires: 29 pp.

Ref HAL: hal-00333879_v1
Ref Arxiv: 0810.3020
DOI: 10.1088/1126-6708/2009/01/033
WoS: 000265578400033
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38 Citations
Résumé:

This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integrals.

Ref HAL: hal-00286513_v1
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Nous calculons des fonctions de corrélation de champs d'intérêt physique pour des modèles sur réseau sous-critiques en adoptant la méthode des opérateurs de vertex sur réseau et nous montrons que les résultats coïncident avec les expressions dérivées par les méthodes de Théories Conformes perturbées.