864 research outputs found
Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
We prove the existence and associativity of the nonmeromorphic operator
product expansion for an infinite family of vertex operator algebras, the
triplet W-algebras, using results from P(z)-tensor product theory. While doing
this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is
improved and one reference is adde
The influence of the strength of bone on the deformation of acetabular shells : a laboratory experiment in cadavers
Date of Acceptance: 24/08/2014 ©2015 The British Editorial Society of Bone & Joint Surgery. The authors would like to thank N. Taylor (3D Measurement Company) for his work with regard to data acquisition and processing of experimental data. We would also like to thank Dr A. Blain of Newcastle University for performing the statistical analysis The research was supported by the NIHR Newcastle Biomedical Research Centre. The authors P. Dold, M. Flohr and R. Preuss are employed by Ceramtec GmbH. Martin Bone received a salary from the joint fund. The author or one or more of the authors have received or will receive benefits for personal or professional use from a commercial party related directly or indirectly to the subject of this article. This article was primary edited by G. Scott and first proof edited by J. Scott.Peer reviewedPostprin
Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
We generalize the string functions C_{n,r}(tau) associated with the coset
^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau)
associated with the coset W(k)/u(1) of the W-algebra of the logarithmically
extended ^sl(2)_k conformal field model with positive integer k. The higher
string functions occur in decomposing W(k) characters with respect to level-k
theta and Appell functions and their derivatives (the characters are neither
quasiperiodic nor holomorphic, and therefore cannot decompose with respect to
only theta-functions). The decomposition coefficients, to be considered
``logarithmic parafermionic characters,'' are given by A_{n,r}(tau),
B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra
characters of the (p=k+2,1) logarithmic model. We study the properties of
A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string
functions C_{n,r}, and evaluate the modular group representation generated from
A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular
transformations of the higher-level Appell functions and the associated
transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some
nonsense in B.3.3. correcte
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
The N=1 triplet vertex operator superalgebras
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras
SW(m), , which are natural super analogs of the triplet vertex
algebra family W(p), , important in logarithmic conformal field
theory. We classify irreducible SW(m)-modules and discuss logarithmic modules.
We also compute bosonic and fermionic formulas of irreducible SW(m) characters.
Finally, we contemplate possible connections between the category of
SW(m)-modules and the category of modules for the quantum group
U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on
properties of characters and the Zhu's algebra A(SW(m)). This paper is a
continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version,
to appear in CM
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.
Wind on the boundary for the Abelian sandpile model
We continue our investigation of the two-dimensional Abelian sandpile model
in terms of a logarithmic conformal field theory with central charge c=-2, by
introducing two new boundary conditions. These have two unusual features: they
carry an intrinsic orientation, and, more strangely, they cannot be imposed
uniformly on a whole boundary (like the edge of a cylinder). They lead to seven
new boundary condition changing fields, some of them being in highest weight
representations (weights -1/8, 0 and 3/8), some others belonging to
indecomposable representations with rank 2 Jordan cells (lowest weights 0 and
1). Their fusion algebra appears to be in full agreement with the fusion rules
conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure
Modular differential equations for torus one-point functions
It is shown that in a rational conformal field theory every torus one-point
function of a given highest weight state satisfies a modular differential
equation. We derive and solve these differential equations explicitly for some
Virasoro minimal models. In general, however, the resulting amplitudes do not
seem to be expressible in terms of standard transcendental functions.Comment: 19 pages, LaTeX; reference adde
Temperley-Lieb Stochastic Processes
We discuss one-dimensional stochastic processes defined through the
Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary
conditions, we formulate a conjecture relating the probability distribution
which describes the stationary state, to the enumeration of a symmetry class of
alternating sign matrices, objects that have received much attention in
combinatorics.Comment: 9 pages LaTeX, 11 Postscript figures, minor change
Association of Early Introduction of Solids With Infant Sleep: A Secondary Analysis of a Randomized Clinical Trial.
Importance: The World Health Organization recommends exclusive breastfeeding for 6 months. However, 75% of British mothers introduce solids before 5 months and 26% report infant waking at night as influencing this decision. Objective: To determine whether early introduction of solids influences infant sleep. Design, Setting, and Participants: The Enquiring About Tolerance study was a population-based randomized clinical trial conducted from January 15, 2008, to August 31, 2015, that included 1303 exclusively breastfed 3-month-old infants from England and Wales. Clinical visits took place at St Thomas' Hospital, London, England, and the trial studied the early introduction of solids into the infant diet from age 3 months. Interventions: The early introduction group (EIG) continued to breastfeed while nonallergenic and then 6 allergenic foods were introduced. The standard introduction group (SIG) followed British infant feeding guidelines (ie, exclusive breastfeeding to around age 6 months and to avoid any food consumption during this period). Main Outcomes and Measures: Secondary analysis of an a priori secondary outcome of the effect of early food introduction on infant sleep using the standardized Brief Infant Sleep Questionnaire. Results: Of the 1303 infants who were enrolled in the Enquiring About Tolerance study, 1225 participants (94%) completed the final 3-year questionnaire (618 SIG [95%] and 607 EIG [93%]). Randomization was effective and there were no significant baseline differences between the 2 groups. Following the early introduction of solids, infants in the EIG slept significantly longer and woke significantly less frequently than infants in the SIG. Differences between the 2 groups peaked at age 6 months. At this point, in the intention-to-treat analysis infants in the EIG slept for 16.6 (95% CI, 7.8-25.4) minutes longer per night and their night waking frequency had decreased from 2.01 to 1.74 wakings per night. Most clinically important, very serious sleep problems, which were significantly associated with maternal quality of life, were reported significantly more frequently in the SIG than in the EIG (odds ratio, 1.8; 95% CI, 1.22-2.61). Conclusions and Relevance: In a randomized clinical trial, the early introduction of solids into the infant's diet was associated with longer sleep duration, less frequent waking at night, and a reduction in reported very serious sleep problems. Trial Registration: isrctn.org Identifier: ISRCTN14254740
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