346 research outputs found
Height variables in the Abelian sandpile model: scaling fields and correlations
We compute the lattice 1-site probabilities, on the upper half-plane, of the
four height variables in the two-dimensional Abelian sandpile model. We find
their exact scaling form when the insertion point is far from the boundary, and
when the boundary is either open or closed. Comparing with the predictions of a
logarithmic conformal theory with central charge c=-2, we find a full
compatibility with the following field assignments: the heights 2, 3 and 4
behave like (an unusual realization of) the logarithmic partner of a primary
field with scaling dimension 2, the primary field itself being associated with
the height 1 variable. Finite size corrections are also computed and
successfully compared with numerical simulations. Relying on these field
assignments, we formulate a conjecture for the scaling form of the lattice
2-point correlations of the height variables on the plane, which remain as yet
unknown. The way conformal invariance is realized in this system points to a
local field theory with c=-2 which is different from the triplet theory.Comment: 68 pages, 17 figures; v2: published version (minor corrections, one
comment added
Fibromatosis of the Plantar Fascia: Diagnosis and Indications For Surgical Treatment
Plantar fibromatosis is a rare, benign lesion involving the plantar aponeurosis. Eleven patients (13 feet) underwent 24 operations, including local excision, wide excision, or complete plantar fasciectomy. Clinical results were evaluated retrospectively. There were no differences among the subgroups in postoperative complications. Two primary fasciectomies did not recur. Three of six revised fasciectomies, seven of nine wide excisions, and six of seven local excisions recurred. Our results indicate that recurrence of plantar fibromatosis after surgical resection can be reduced by aggressive initial surgical resection
Prevailing impacts of river management on microplastic transport in contrasting US streams:rethinking global microplastic flux estimations
Timelike Boundary Liouville Theory
The timelike boundary Liouville (TBL) conformal field theory consisting of a
negative norm boson with an exponential boundary interaction is considered. TBL
and its close cousin, a positive norm boson with a non-hermitian boundary
interaction, arise in the description of the accumulation point of
minimal models, as the worldsheet description of open string tachyon
condensation in string theory and in scaling limits of superconductors with
line defects. Bulk correlators are shown to be exactly soluble. In contrast,
due to OPE singularities near the boundary interaction, the computation of
boundary correlators is a challenging problem which we address but do not fully
solve. Analytic continuation from the known correlators of spatial boundary
Liouville to TBL encounters an infinite accumulation of poles and zeros. A
particular contour prescription is proposed which cancels the poles against the
zeros in the boundary correlator d(\o) of two operators of weight \o^2 and
yields a finite result. A general relation is proposed between two-point CFT
correlators and stringy Bogolubov coefficients, according to which the
magnitude of d(\o) determines the rate of open string pair creation during
tachyon condensation. The rate so obtained agrees at large \o with a
minisuperspace analysis of previous work. It is suggested that the mathematical
ambiguity arising in the prescription for analytic continuation of the
correlators corresponds to the physical ambiguity in the choice of open string
modes and vacua in a time dependent background.Comment: 28 pages, 1 figure, v2 reference and acknowledgement adde
Constructing Gauge Theory Geometries from Matrix Models
We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa
in order to construct the geometry encoding the exact gaugino condensate
superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or
anti-symmetric matter, broken by a tree level superpotential to a product
subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant
geometry is encoded by a non-hyperelliptic Riemann surface, which we extract
from the exact loop equations. We also show that O(1/N) corrections can be
extracted from a logarithmic deformation of this surface. The loop equations
contain explicitly subleading terms of order 1/N, which encode information of
string theory on an orientifolded local quiver geometry.Comment: 52 page
Energy Quantisation in Bulk Bouncing Tachyon
We argue that the closed string energy in the bulk bouncing tachyon
background is to be quantised in a simple manner as if strings were trapped in
a finite time interval. We discuss it from three different viewpoints; (1) the
timelike continuation of the sinh-Gordon model, (2) the dual matrix model
description of the (1+1)-dimensional string theory with the bulk bouncing
tachyon condensate, (3) the c_L=1 limit of the timelike Liouville theory with
the dual Liouville potential turned on. There appears to be a parallel between
the bulk bouncing tachyon and the full S-brane of D-brane decay. We find the
critical value \lambda_c of the bulk bouncing tachyon coupling which is
analogous to \lambda_o=1/2 of the full S-brane coupling, at which the system is
thought to be at the bottom of the tachyon potential.Comment: 25 pages, minor changes, one reference adde
AQFT from n-functorial QFT
There are essentially two different approaches to the axiomatization of
quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and
functorial QFT, going back to Atiyah and Segal. More recently, based on ideas
by Baez and Dolan, the latter is being refined to "extended" functorial QFT by
Freed, Hopkins, Lurie and others. The first approach uses local nets of
operator algebras which assign to each patch an algebra "of observables", the
latter uses n-functors which assign to each patch a "propagator of states".
In this note we present an observation about how these two axiom systems are
naturally related: we demonstrate under mild assumptions that every
2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport")
naturally yields a local net. This is obtained by postcomposing the propagation
2-functor with an operation that mimics the passage from the Schroedinger
picture to the Heisenberg picture in quantum mechanics.
The argument has a straightforward generalization to general
pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic
inclusion of subfactors; references adde
The fusion algebra of bimodule categories
We establish an algebra-isomorphism between the complexified Grothendieck
ring F of certain bimodule categories over a modular tensor category and the
endomorphism algebra of appropriate morphism spaces of those bimodule
categories. This provides a purely categorical proof of a conjecture by Ostrik
concerning the structure of F.
As a by-product we obtain a concrete expression for the structure constants
of the Grothendieck ring of the bimodule category in terms of endomorphisms of
the tensor unit of the underlying modular tensor category.Comment: 16 page
Conformal Field Theories, Graphs and Quantum Algebras
This article reviews some recent progress in our understanding of the
structure of Rational Conformal Field Theories, based on ideas that originate
for a large part in the work of A. Ocneanu. The consistency conditions that
generalize modular invariance for a given RCFT in the presence of various types
of boundary conditions --open, twisted-- are encoded in a system of integer
multiplicities that form matrix representations of fusion-like algebras. These
multiplicities are also the combinatorial data that enable one to construct an
abstract ``quantum'' algebra, whose - and -symbols contain essential
information on the Operator Product Algebra of the RCFT and are part of a cell
system, subject to pentagonal identities. It looks quite plausible that the
classification of a wide class of RCFT amounts to a classification of ``Weak
- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001
--Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in
Math., Birkhauser. References and comments adde
Rolling Tachyons from Liouville theory
In this work we propose an exact solution of the c=1 Liouville model, i.e. of
the world-sheet theory that describes the homogeneous decay of a closed string
tachyon. Our expressions are obtained through careful extrapolation from the
correlators of Liouville theory with c > 25. In the c=1 limit, we find two
different theories which differ by the signature of Liouville field. The
Euclidean limit coincides with the interacting c=1 theory that was constructed
by Runkel and Watts as a limit of unitary minimal models. The couplings for the
Lorentzian limit are new. In contrast to the behavior at c > 1, amplitudes in
both c=1 models are non-analytic in the momenta and consequently they are not
related by Wick rotation.Comment: 22 page
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