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

Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories

We reexamine in detail the problem of fermions interacting with a non-Abelian random vector potential. Without resorting to the replica or supersymmetry approaches, we show that in the limit of infinite disorder strength the theory possesses an exact solution which takes the form of a logarithmic conformal field theory. We show that the proper treatment of the locality conditions in the SU(2) theory leads to the termination of the multifractal spectrum, or in other words to the termination of the infinite hierarchies of negative-dimensional operators that were thought to occur. Based on arguments of logarithmic degeneracies, we conjecture that such a termination mechanism should be present for general SU(N). Moreover, our results lead to the conclusion that the previous replica solution of this problem yields incorrect results.Comment: Revised version, to appear in Nucl. Phys.

A survey of the treatment and management of patients with severe chronic spontaneous urticaria.

Chronic spontaneous urticaria (CSU) is characterized by the recurrent appearance of weals, angio‐oedema or both, occurring at least twice weekly for longer than 6 weeks.1 It is often managed with antihistamines, but occasionally requires other systemic agents in recalcitrant cases. A cross‐sectional survey was conducted by means of an internet‐based survey tool (Typeform; https://www.typeform.com). Participating consultants with a specialist interest in urticaria were identified through the specialist registers of the British Society of Allergy and Clinical Immunology (BSACI), the Improving Quality in Allergy Services (IQAS) Group and the British Association of Dermatologists (BAD), and invited to take part. The survey content was based on current CSU treatment guidelines from EAACI/GA2LEN/EDF/WAO1 and the British Society for Allergy and Clinical Immunology (BSACI).2 The EAACI/GA2LEN/EDF/WAO guidelines are a joint initiative of the Dermatology Section of the European Academy of Allergy and Clinical Immunology (EAACI), the Global Allergy and Asthma European Network (GA2LEN) (a European Union‐funded network of excellence), the European Dermatology Forum (EDF), and the World Allergy Organization (WAO). To standardize responses, all participants were presented with a case of recalcitrant CSU (failed on maximum dose of nonsedating antihistamines and montelukast), requiring alternative systemic treatment. Questions covered usage of systemic treatments, routine disease severity assessments, adherence to treatment guidelines and perceived barriers to prescribing. Responses (Table 1) were received from 19 UK consultants (26 surveys sent; completion rate 73%), 15 of whom had > 10 years’ experience in the treatment of CSU. The majority were allergy (58%) and dermatology consultants (37%). Of the 19 consultants, 56% provide a dedicated urticaria service, 37% treat both adult and paediatric patients, and the majority (79%) use systemic medications other than antihistamines and montelukast. Omalizumab and ciclosporin were the most commonly used first‐line agents (47% and 27% respectively) (Fig. 1). The majority (84%) of consultants use validated measures to assess disease severity, including the weekly Urticaria Activity Score (UAS‐7, 63%), the Physician Global Assessment (63%), the Patient Global Assessment (44%) and the Dermatology Quality of Life Index (DLQI) (38%). Guidelines are used by 89% to direct their management of CSU, with 50% using the EAACI/GA2LEN/EDF/WAO guideline,1 compared with 31% primarily using the BSACI guideline.2 The main perceived barriers to prescribing systemic medications were potential adverse effects (AEs) (32% strongly agreed), potential long‐term toxicity (26% strongly agreed), cost of treatment (42% strongly agreed), and views expressed by the patient and their family (37% agreed)

Logarithmic intertwining operators and vertex operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1)_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1)_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM

On conformal Jordan cells of finite and infinite rank

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering cell of the same weight but infinite rank.Comment: 9 pages, LaTeX, v2: typo corrected, comments added, version to be publishe

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

Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)

Using explicit results for the four-point correlation functions of the Wess-Zumino-Novikov-Witten (WZNW) model we discuss the conformal embedding osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0). This embedding has emerged in Bernard and LeClair's recent paper [1]. Given that the osp(4|4)_(1) WZNW model is a free theory with power law correlation functions, whereas the su(2)_(0) and osp(2|2)_(-2) models are CFTs with logarithmic correlation functions, one immediately wonders whether or not it is possible to combine these logarithms and obtain simple power laws. Indeed, this very concern has been raised in a revised version of [1]. In this paper we demonstrate how one may recover the free field behaviour from a braiding of the solutions of the su(2)_(0) and osp(2|2)_(-2) Knizhnik-Zamolodchikov equations. We do this by implementing a procedure analogous to the conformal bootstrap programme [2]. Our ability to recover such simple behaviour relies on a remarkable identity in the theory of elliptic integrals known as Legendre's relation.Comment: 13 pages, RevTe

Extended chiral algebras in the SU(2)_0 WZNW model

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde

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

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference