32 research outputs found
Null vectors of the W_3 algebra
We construct null vectors of a restricted class explicitly in two
different forms. The method we use is an extension of that of Bauer et al.~in
the Virasoro case. Our results are analogous to the formulae of Benoit and
St.~Aubin for the Virasoro null vectors. We derive in the Virasoro case some
alternative formulae for the same null vectors involving only the and
modes of the Virasoro algebra. }Comment: 8 pages, LaTeX, EFI-92-50, DAMTP-92-62 (second version - slight TeX
error in first version
G_2^1 Affine Toda Field Theory: A Numerical Test of Exact S-Matrix results
We present the results of a Monte--Carlo simulation of the Affine
Toda field theory action in two dimensions. We measured the ratio of the masses
of the two fundamental particles as a function of the coupling constant. Our
results strongly support the conjectured duality with the theory,
and are consistent with the mass formula of Delius et al.Comment: 5 pages, LaTeX, DTP-9223, DAMTP-92-4
A Note of W-algebra Realisations
We provide a general description of realisations of W--algebras in terms of
smaller W--algebras and free fields. This is based on the definition of the
W--algebra as the commutant of a set of screening charges. This is conjectured
to be related to partial gauge-fixings in the Hamiltonian reduction model.Comment: 8 page
On Perturbations of Unitary Minimal Models by Boundary Condition Changing Operators
In this note we consider boundary perturbations in the A-Series unitary
minimal models by phi_{r,r+2} fields on superpositions of boundaries. In
particular, we consider perturbations by boundary condition changing operators.
Within conformal perturbation theory we explicitly map out the space of
perturbative renormalisation group flows for the example phi_{1,3} and find
that this sheds light on more general phi_{r,r+2} perturbations. Finally, we
find a simple diagrammatic representation for the space of flows from a single
Cardy boundary condition.Comment: 27 pages, 10 figure
Minimal model boundary flows and c=1 CFT
We consider perturbations of unitary minimal models by boundary fields.
Initially we consider the models in the limit as c -> 1 and find that the
relevant boundary fields all have simple interpretations in this limit. This
interpretation allows us to conjecture the IR limits of flows in the unitary
minimal models generated by the fields \phi_{rr} of `low' weight. We check this
conjecture using the truncated conformal space approach. In the process we find
evidence for a new series of integrable boundary flows.Comment: (latex2e, 27 pages, 17 figures
Twisted algebra R-matrices and S-matrices for affine Toda solitons and their bound states
We construct new and invariant
-matrices and comment on the general construction of -matrices for
twisted algebras. We use the former to construct -matrices for
affine Toda solitons and their bound states, identifying the lowest breathers
with the particles.Comment: Latex, 24 pages. Various misprints corrected. New section added
clarifying relationship between R-matrices and S-matrice
Quantum mass corrections for affine Toda solitons
We calculate the first quantum corrections to the masses of solitons in
imaginary-coupling affine Toda theories using the semi-classical method of
Dashen, Hasslacher and Neveu. The theories divide naturally into those based on
the simply-laced, the twisted and the untwisted non-simply-laced algebras. We
find that the classical relationships between soliton and particle masses found
by Olive {\em et al.\ }persist for the first two classes, but do not appear to
do so naively for the third.Comment: 39pp, .uu compressed dvifile. Revised version alters two references
and includes hep-th no. on Title pag
The conformal boundary states for SU(2) at level 1
For the case of the SU(2) WZW model at level one, the boundary states that
only preserve the conformal symmetry are analysed. Under the assumption that
the usual Cardy boundary states as well as their marginal deformations are
consistent, the most general conformal boundary states are determined. They are
found to be parametrised by group elements in SL(2,C).Comment: 22 pages, harvmac (b), 5 figure
Bicategories for boundary conditions and for surface defects in 3-d TFT
We analyze topological boundary conditions and topological surface defects in
three-dimensional topological field theories of Reshetikhin-Turaev type based
on arbitrary modular tensor categories. Boundary conditions are described by
central functors that lift to trivializations in the Witt group of modular
tensor categories. The bicategory of boundary conditions can be described
through the bicategory of module categories over any such trivialization. A
similar description is obtained for topological surface defects. Using string
diagrams for bicategories we also establish a precise relation between special
symmetric Frobenius algebras and Wilson lines involving special defects. We
compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong
on boundary conditions and surface defects in abelian Chern-Simons theories and
in Turaev-Viro type TFTs, respectively.Comment: 34 pages, some figures. v2: references added. v3: typos corrected and
biliography update
Universality of the Crossing Probability for the Potts Model for q=1,2,3,4
The universality of the crossing probability of a system to
percolate only in the horizontal direction, was investigated numerically by
using a cluster Monte-Carlo algorithm for the -state Potts model for
and for percolation . We check the percolation through
Fortuin-Kasteleyn clusters near the critical point on the square lattice by
using representation of the Potts model as the correlated site-bond percolation
model. It was shown that probability of a system to percolate only in the
horizontal direction has universal form for
as a function of the scaling variable . Here,
is the probability of a bond to be closed, is the
nonuniversal crossing amplitude, is the nonuniversal metric factor,
is the nonuniversal scaling index, is the correlation
length index.
The universal function . Nonuniversal scaling factors
were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed,
journal-ref added