731 research outputs found
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
Fermion-boson duality in integrable quantum field theory
We introduce and study one parameter family of integrable quantum field
theories. This family has a Lagrangian description in terms of massive Thirring
fermions and charged bosons of complex
sinh-Gordon model coupled with affine Toda theory. Perturbative
calculations, analysis of the factorized scattering theory and the Bethe ansatz
technique are applied to show that under duality transformation, which relates
weak and strong coupling regimes of the theory the fermions
transform to bosons and and vive versa.
The scattering amplitudes of neutral particles in this theory coincide exactly
with S-matrix of particles in pure
Toda theory, i.e. the contribution of charged bosons and fermions to these
amplitudes exactly cancel each other. We describe and discuss the symmetry
responsible for this compensation property.Comment: 12 pages, LaTex file with amste
Magnetoresistance in the s-d Model with Arbitrary Impurity Spin
The magnetoresistance, the number of the localized electrons, and the s-wave
scattering phase shift at the Fermi level for the s-d model with arbitrary
impurity spin are obtained in the ground state. To obtain above results some
known exact results of the Bethe ansatz method are used. As the impurity spin S
= 1/2, our results coincide with those obtained by Ishii \textit{et al%}. The
compairsion between the theoretical and experimental magneticresistence for
impurity S = 1/2 is re-examined.Comment: 6 pages, 2 figure
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
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
Boundary One-Point Functions, Scattering, and Background Vacuum Solutions in Toda Theories
The parametric families of integrable boundary affine Toda theories are
considered. We calculate boundary one-point functions and propose boundary
S-matrices in these theories. We use boundary one-point functions and S-matrix
amplitudes to derive boundary ground state energies and exact solutions
describing classical vacuum configurations.Comment: 20 pages, 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
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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