972 research outputs found

### 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

### 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

### 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

### A Note on Z_2 Symmetries of the KZ Equation

We continue the study of hidden Z_2 symmetries of the four-point sl(2)_k
Knizhnik-Zamolodchikov equation iniciated in hep-th/0508019. Here, we focus our
attention on the four-point correlation function in those cases where one
spectral flowed state of the sector w=1 is involved. We give a formula that
shows how this observable can be expressed in terms of the four-point function
of non spectral flowed states. This means that the formula holding for the
winding violating four-string scattering processes in AdS_3 has a simple
expression in terms of the one for the conservative case, generalizing what is
known for the case of three-point functions, where the violating and the
non-violating structure constants turn out to be connected one to each other in
a similar way. What makes this connection particularly simple is the fact that,
unlike what one would naively expect, it is not necessary to explicitly solve
the five-point function containing a single spectral flow operator to this end.
Instead, non diagonal functional relations between different solutions of the
KZ equation turn out to be the key point for this short path to exist.
Considering such functional relation is necessary but it is not sufficient;
besides, the formula also follows from the relation existing between
correlators in both WZNW and Liouville conformal theories.Comment: 24 pages. Minor changes and references added; version accepted for
publicatio

### 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

### 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

### On scaling fields in $Z_N$ Ising models

We study the space of scaling fields in the $Z_N$ symmetric models with the
factorized scattering and propose simplest algebraic relations between form
factors induced by the action of deformed parafermionic currents. The
construction gives a new free field representation for form factors of
perturbed Virasoro algebra primary fields, which are parafermionic algebra
descendants. We find exact vacuum expectation values of physically important
fields and study correlation functions of order and disorder fields in the form
factor and CFT perturbation approaches.Comment: 2 Figures, jetpl.cl

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