Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality

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

The Higgs and Coulomb/Confining Phases in "Twisted-Mass" Deformed CP(N-1) Model

We consider non-supersymmetric two-dimensional CP(N-1) model deformed by a term presenting the bosonic part of the twisted mass deformation of N=2 supersymmetric version of the model. Our deformation has a special form preserving a Z_N symmetry at the Lagrangian level. In the large mass limit the model is weakly coupled. Its dynamics is described by the Higgs phase, with Z_N spontaneously broken. At small masses it is in the strong coupling Coulomb/confining phase. The Z_N symmetry is restored. Two phases are separated by a phase transition. We find the phase transition point in the large-N limit. It lies at strong coupling. As was expected, the phase transition is related to broken versus unbroken Z_N symmetry in these two respective phases. The vacuum energies for these phases are determined too.Comment: 20 pages, 3 figures, reference adde

On AGT conjecture

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.Comment: References adde

Correlation functions in conformal Toda field theory I

Two-dimensional sl(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the three-point correlation functions of the exponential fields if one of the three fields has a special form. In this case it is possible to write down and solve explicitly the differential equation for the four-point correlation function if the fourth field is completely degenerate. We give also expressions for the three-point correlation functions in the cases, when they can be expressed in terms of known functions. The semiclassical and minisuperspace approaches in the conformal Toda field theory are studied and the results coming from these approaches are compared with the proposed analytical expression for the three-point correlation function. We show, that in the framework of semiclassical and minisuperspace approaches general three-point correlation function can be reduced to the finite-dimensional integral.Comment: 54 pages, JHEP styl

Multipoint correlation functions in Liouville field theory and minimal Liouville gravity

We study n+3-point correlation functions of exponential fields in Liouville field theory with n degenerate and 3 arbitrary fields. An analytical expression for these correlation functions is derived in terms of Coulomb integrals. The application of these results to the minimal Liouville gravity is considered.Comment: Contribution to the proceedings of the International Workshop on Classical and Quantum Integrable Systems, Dubna, Russia, January 22-25, 2007, 18 page

Miura-Like Free Field Realization Of Fermionic Casimir WB(3) Algebras

Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B(3),we give an explicit construction of the Casimir WB(3) algebras.We reserve the notation WB(N) for the Casimir W algebras of type W(2,4,6,...,2N,N+1/2) which contains one fermionic field. It is seen that WB(3) algebra is closed an associative for all values of the central element c.Comment: 7 pages,no figures,TeX fil

Vertex Operator Extension of Casimir W A(N) Algebras

We give an extension of Casimir of Casimir $\cal{WA_N}$ algebras including a vertex operator which depends on non-simple roots of $A_{N-1}$.Comment: 7 pages,no figures,TeX file,(to appear in Mod.Phys.Lett.A