6,641 research outputs found
Boundary operators in the O(n) and RSOS matrix models
We study the new boundary condition of the O(n) model proposed by Jacobsen
and Saleur using the matrix model. The spectrum of boundary operators and their
conformal weights are obtained by solving the loop equations. Using the
diagrammatic expansion of the matrix model as well as the loop equations, we
make an explicit correspondence between the new boundary condition of the O(n)
model and the "alternating height" boundary conditions in RSOS model.Comment: 29 pages, 4 figures; version to appear in JHE
Stress Energy Tensor in c=0 Logarithmic Conformal Field Theory
We discuss the partners of the stress energy tensor and their structure in
Logarithmic conformal field theories. In particular we draw attention to the
fundamental differences between theories with zero and non-zero central charge.
We analyze the OPE for T, \bar{T} and the logarithmic partners t and \bar{t}
for c=0 theories.Comment: LATEX 14 pages. Contribution to the Michael Marinov Memorial Volum
Boundary changing operators in the O(n) matrix model
We continue the study of boundary operators in the dense O(n) model on the
random lattice. The conformal dimension of boundary operators inserted between
two JS boundaries of different weight is derived from the matrix model
description. Our results are in agreement with the regular lattice findings. A
connection is made between the loop equations in the continuum limit and the
shift relations of boundary Liouville 3-points functions obtained from Boundary
Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve
Structure of the two-boundary XXZ model with non-diagonal boundary terms
We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction
Equivalences between spin models induced by defects
The spectrum of integrable spin chains are shown to be independent of the
ordering of their spins. As an application we introduce defects (local spin
inhomogeneities in homogenous chains) in two-boundary spin systems and, by
changing their locations, we show the spectral equivalence of different
boundary conditions. In particular we relate certain nondiagonal boundary
conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio
Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
We discuss the partners of the stress energy tensor and their structure in
Logarithmic conformal field theories. In particular we draw attention to the
fundamental differences between theories with zero and non-zero central charge.
However they are both characterised by at least two independent parameters. We
show how, by using a generalised Sugawara construction, one can calculate the
logarithmic partner of T. We show that such a construction works in the c=-2
theory using the conformal dimension one primary currents which generate a
logarithmic extension of the Kac-Moody algebra.Comment: 19 pages. Minor correction
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
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