845 research outputs found
The third parafermionic chiral algebra with the symmetry Z_{3}
We have constructed the parafermionic chiral algebra with the principal
parafermionic fields \Psi,\Psi^{+} having the conformal dimension
\Delta_{\Psi}=8/3 and realizing the symmetry Z_{3}.Comment: 6 pages, no figur
Parafermionic theory with the symmetry Z_5
A parafermionic conformal theory with the symmetry Z_5 is constructed, based
on the second solution of Fateev-Zamolodchikov for the corresponding
parafermionic chiral algebra.
The primary operators of the theory, which are the singlet, doublet 1,
doublet 2, and disorder operators, are found to be accommodated by the weight
lattice of the classical Lie algebra B_2. The finite Kac tables for unitary
theories are defined and the formula for the conformal dimensions of primary
operators is given.Comment: 98 pages, 21 eps figure
Conformal field theories with Z_N and Lie algebra symmetries
We construct two-dimensional conformal field theories with a Z_N symmetry,
based on the second solution of Fateev-Zamolodchikov for the parafermionic
chiral algebra. Primary operators are classified according to their
transformation properties under the dihedral group (Z_N x Z_2, where Z_2 stands
for the Z_N charge conjugation), as singlets, [(N-1)/2] different doublets, and
a disorder operator. In an assumed Coulomb gas scenario, the corresponding
vertex operators are accommodated by the Kac table based on the weight lattice
of the Lie algebra B_{(N-1)/2} when N is odd, and D_{N/2} when N is even. The
unitary theories are representations of the coset SO_n(N) x SO_2(N) /
SO_{n+2}(N), with n=1,2,.... We suggest that physically they realize the series
of multicritical points in statistical systems having a Z_N symmetry.Comment: 4 pages, 2 figure
Parafermionic theory with the symmetry Z_N, for N odd
We construct a parafermionic conformal theory with the symmetry Z_N, for N
odd, based on the second solution of Fateev-Zamolodchikov for the corresponding
parafermionic chiral algebra. Primary operators are classified according to
their transformation properties under the dihedral group D_N, as singlet,
doublet 1,2,...,(N-1)/2, and disorder operators. In an assumed Coulomb gas
scenario, the corresponding vertex operators are accommodated by the weight
lattice of the Lie algebra B_(N-1)/2. The unitary theories are representations
of the coset SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,... . Physically, they
realise the series of multicritical points in statistical theories having a D_N
symmetry.Comment: 34 pages, 1 figure. v2: note added in proo
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
Renormalization group flows for the second parafermionic field theory for N odd
Using the renormalization group approach, the Coulomb gas and the coset
techniques, the effect of slightly relevant perturbations is studied for the
second parafermionic field theory with the symmetry , for N odd. New
fixed points are found and classified
Parafermionic theory with the symmetry Z_N, for N even
Following our previous papers (hep-th/0212158 and hep-th/0303126) we complete
the construction of the parafermionic theory with the symmetry Z_N based on the
second solution of Fateev-Zamolodchikov for the corresponding parafermionic
chiral algebra. In the present paper we construct the Z_N parafermionic theory
for N even. Primary operators are classified according to their transformation
properties under the dihedral group (Z_N x Z_2, where Z_2 stands for the Z_N
charge conjugation), as two singlets, doublet 1,2,...,N/2-1, and a disorder
operator. In an assumed Coulomb gas scenario, the corresponding vertex
operators are accommodated by the Kac table based on the weight lattice of the
Lie algebra D_{N/2}. The unitary theories are representations of the coset
SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,.... We suggest that physically
they realise the series of multicritical points in statistical systems having a
Z_N symmetry
Conformal Toda theory with a boundary
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>2) 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>2) 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 B"acklund
transformation for sl(3) Toda classical mechanics, using the minisuperspace
limit of the bulk one-point function.Comment: 42 pages; version 4: added clarifications in section 2.2 and
footnotes 1 and
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
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