330 research outputs found
SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
We show that the SU(2)_0 WZNW model has a hidden OSp(2|2)_{-2} symmetry. Both
these theories are known to have logarithms in their correlation functions. We
also show that, like OSp(2|2)_{-2}, the logarithmic structure present in the
SU(2)_0 model is due to the underlying c=-2 sector. We also demonstrate that
the quantum Hamiltonian reduction of SU(2)_0 leads very directly to the
correlation functions of the c=-2 model. We also discuss some of the novel
boundary effects which can take place in this model.Comment: 31 pages. Revised versio
Integrable Perturbations of and WZW Models
We present a new class of 2d integrable models obtained as perturbations of
minimal CFT with W-symmetry by fundamental weight primaries. These models are
generalisations of well known -perturbed Virasoro minimal models. In the
large (number of minimal model) limit they coincide with scalar
perturbations of WZW theories. The algebra of conserved charges is discussed in
this limit. We prove that it is noncommutative and coincides with twisted
affine algebra represented in a space of asymptotic states. We conjecture
that scattering in these models for generic is described by -matrix of
the -deformed - algebra with being root of unity.Comment: 10p., LaTeX, preprint SISSA 19/94/FM (references added
World-Sheet Logarithmic Operators and Target Space Symmetries in String Theory
We discuss the target-space interpretation of the world-sheet logarithmic
operators in string theory. These operators generate the normalizable zero
modes (discrete states) in target space, which restore the symmetries of the
theory broken by the background. The problem of the recoil in string theory is
considered, as well as some general properties of string amplitudes containing
logarithmic operators.Comment: 22 pages, LaTeX, some minor corrections and references adde
Origin of Logarithmic Operators in Conformal Field Theories
We study logarithmic operators in Coulomb gas models, and show that they
occur when the ``puncture'' operator of the Liouville theory is included in the
model. We also consider WZNW models for , and for SU(2) at level 0, in
which we find logarithmic operators which form Jordan blocks for the current as
well as the Virasoro algebra.Comment: 22 pages Latex. Some references adde
Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory
The model of dense lattice polymers is studied as an example of non-unitary
Conformal Field Theory (CFT) with . ``Antisymmetric'' correlation
functions of the model are proved to be given by the generalized Kirchhoff
theorem. Continuous limit of the model is described by the free complex
Grassmann field with null vacuum vector. The fundamental property of the
Grassmann field and its twist field (both having non-positive conformal
weights) is that they themselves suppress zero mode so that their correlation
functions become non-trivial. The correlation functions of the fields with
positive conformal weights are non-zero only in the presence of the Dirichlet
operator that suppresses zero mode and imposes proper boundary conditions.Comment: 5 pages, REVTeX, remark is adde
Affine Toda Solitons and Vertex Operators
Affine Toda theories with imaginary couplings associate with any simple Lie
algebra generalisations of Sine Gordon theory which are likewise
integrable and possess soliton solutions. The solitons are \lq\lq created" by
exponentials of quantities which lie in the untwisted affine
Kac-Moody algebra and ad-diagonalise the principal Heisenberg
subalgebra. When is simply-laced and highest weight irreducible
representations at level one are considered, can be expressed as
a vertex operator whose square vanishes. This nilpotency property is extended
to all highest weight representations of all affine untwisted Kac-Moody
algebras in the sense that the highest non vanishing power becomes proportional
to the level. As a consequence, the exponential series mentioned terminates and
the soliton solutions have a relatively simple algebraic expression whose
properties can be studied in a general way. This means that various physical
properties of the soliton solutions can be directly related to the algebraic
structure. For example, a classical version of Dorey's fusing rule follows from
the operator product expansion of two 's, at least when is
simply laced. This adds to the list of resemblances of the solitons with
respect to the particles which are the quantum excitations of the fields.Comment: Imperial/TP/92-93/29 SWAT/92-93/5 PU-PH-93/1392, requires newma
Integrals of Motion for Critical Dense Polymers and Symplectic Fermions
We consider critical dense polymers . We obtain for this model
the eigenvalues of the local integrals of motion of the underlying Conformal
Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed
description of the relation between this model and Symplectic Fermions
including the indecomposable structure of the transfer matrix. Integrals of
motion are defined directly on the lattice in terms of the Temperley Lieb
Algebra and their eigenvalues are obtained and expressed as an infinite sum of
the eigenvalues of the continuum integrals of motion. An elegant decomposition
of the transfer matrix in terms of a finite number of lattice integrals of
motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA
Generalized twisted modules associated to general automorphisms of a vertex operator algebra
We introduce a notion of strongly C^{\times}-graded, or equivalently,
C/Z-graded generalized g-twisted V-module associated to an automorphism g, not
necessarily of finite order, of a vertex operator algebra. We also introduce a
notion of strongly C-graded generalized g-twisted V-module if V admits an
additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a
vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let
u be an element of V of weight 1 such that L(1)u=0. Then the exponential of
2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a
strongly C-graded generalized g_{u}-twisted V-module is constructed from a
strongly C-graded generalized V-module with a compatible action of g_{u} by
modifying the vertex operator map for the generalized V-module using the
exponential of the negative-power part of the vertex operator Y(u, x). In
particular, we give examples of such generalized twisted modules associated to
the exponentials of some screening operators on certain vertex operator
algebras related to the triplet W-algebras. An important feature is that we
have to work with generalized (twisted) V-modules which are doubly graded by
the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for
L(0), and the twisted vertex operators in general involve the logarithm of the
formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on
triplet W-algebras added, misprints corrected, and expositions revise
A differential U-module algebra for U=U_q sl(2) at an even root of unity
We show that the full matrix algebra Mat_p(C) is a U-module algebra for U =
U_q sl(2), a 2p^3-dimensional quantum sl(2) group at the 2p-th root of unity.
Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n with all
odd n, 1<=n<=p. In terms of generators and relations, this U-module algebra is
described as the algebra of q-differential operators "in one variable" with the
relations D z = q - q^{-1} + q^{-2} z D and z^p = D^p = 0. These relations
define a "parafermionic" statistics that generalizes the fermionic commutation
relations. By the Kazhdan--Lusztig duality, it is to be realized in a
manifestly quantum-group-symmetric description of (p,1) logarithmic conformal
field models. We extend the Kazhdan--Lusztig duality between U and the (p,1)
logarithmic models by constructing a quantum de Rham complex of the new
U-module algebra.Comment: 29 pages, amsart++, xypics. V3: The differential U-module algebra was
claimed quantum commutative erroneously. This is now corrected, the other
results unaffecte
From boundary to bulk in logarithmic CFT
The analogue of the charge-conjugation modular invariant for rational
logarithmic conformal field theories is constructed. This is done by
reconstructing the bulk spectrum from a simple boundary condition (the analogue
of the Cardy `identity brane'). We apply the general method to the c_1,p
triplet models and reproduce the previously known bulk theory for p=2 at c=-2.
For general p we verify that the resulting partition functions are modular
invariant. We also construct the complete set of 2p boundary states, and
confirm that the identity brane from which we started indeed exists. As a
by-product we obtain a logarithmic version of the Verlinde formula for the
c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in
J.Phys.
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