900 research outputs found
On AGT conjecture
In these notes we consider relation between conformal blocks and the Nekrasov
partition function of certain SYM theories proposed recently by
Alday, Gaiotto and Tachikawa. We concentrate on theory,
which is the simplest example of AGT relation.Comment: References adde
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
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
On differential equation on four-point correlation function in the Conformal Toda Field Theory
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.Comment: 5 page
On scaling fields in Ising models
We study the space of scaling fields in the 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
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 algebras including a
vertex operator which depends on non-simple roots of .Comment: 7 pages,no figures,TeX file,(to appear in Mod.Phys.Lett.A
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