653 research outputs found
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
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
Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
Liouville field theory on a sphere is considered. We explicitly derive a
differential equation for four-point correlation functions with one degenerate
field . We introduce and study also a class of four-point
conformal blocks which can be calculated exactly and represented by finite
dimensional integrals of elliptic theta-functions for arbitrary intermediate
dimension. We study also the bootstrap equations for these conformal blocks and
derive integral representations for corresponding four-point correlation
functions. A relation between the one-point correlation function of a primary
field on a torus and a special four-point correlation function on a sphere is
proposed
A conformal field theory description of the paired and parafermionic states in the quantum Hall effect
We extend the construction of the effective conformal field theory for the
Jain hierarchical fillings proposed in cond-mat/9912287 to the description of a
quantum Hall fluid at non standard fillings nu=m/(pm+2). The chiral primary
fields are found by using a procedure which induces twisted boundary conditions
on the m scalar fields; they appear as composite operators of a charged and
neutral component. The neutral modes describe parafermions and contribute to
the ground state wave function with a generalized Pfaffian term. Correlators of
Ne electrons in the presence of quasi-hole excitations are explicitly given for
m=2.Comment: 11 pages, plain Late
Null vectors, 3-point and 4-point functions in conformal field theory
We consider 3-point and 4-point correlation functions in a conformal field
theory with a W-algebra symmetry. Whereas in a theory with only Virasoro
symmetry the three point functions of descendants fields are uniquely
determined by the three point function of the corresponding primary fields this
is not the case for a theory with algebra symmetry. The generic 3-point
functions of W-descendant fields have a countable degree of arbitrariness. We
find, however, that if one of the fields belongs to a representation with null
states that this has implications for the 3-point functions. In particular if
one of the representations is doubly-degenerate then the 3-point function is
determined up to an overall constant. We extend our analysis to 4-point
functions and find that if two of the W-primary fields are doubly degenerate
then the intermediate channels are limited to a finite set and that the
corresponding chiral blocks are determined up to an overall constant. This
corresponds to the existence of a linear differential equation for the chiral
blocks with two completely degenerate fields as has been found in the work of
Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4
Lattice algebras and quantum groups
We represent Feigin's construction [22] of lattice W algebras and give some
simple results: lattice Virasoro and algebras. For simplest case
we introduce whole quantum group on this lattice. We
find simplest two-dimensional module as well as exchange relations and define
lattice Virasoro algebra as algebra of invariants of . Another
generalization is connected with lattice integrals of motion as the invariants
of quantum affine group . We show that Volkov's scheme leads
to the system of difference equations for the function from non-commutative
variables.Comment: 13 pages, misprints have been correcte
Conserved charges in the chiral 3-state Potts model
We consider the perturbations of the 3-state Potts conformal field theory
introduced by Cardy as a description of the chiral 3-state Potts model. By
generalising Zamolodchikov's counting argument and by explicit calculation we
find new inhomogeneous conserved currents for this theory. We conjecture the
existence of an infinite set of conserved currents of this form and discuss
their relevance to the description of the chiral Potts models
Correlation functions of disorder fields and parafermionic currents in Z(N) Ising models
We study correlation functions of parafermionic currents and disorder fields
in the Z(N) symmetric conformal field theory perturbed by the first thermal
operator. Following the ideas of Al. Zamolodchikov, we develop for the
correlation functions the conformal perturbation theory at small scales and the
form factors spectral decomposition at large ones. For all N there is an
agreement between the data at the intermediate distances. We consider the
problems arising in the description of the space of scaling fields in perturbed
models, such as null vector relations, equations of motion and a consistent
treatment of fields related by a resonance condition.Comment: 41 pp. v2: some typos and references are corrected
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