Classical Wakimoto Realizations of Chiral WZNW Bloch Waves

It is well-known that the chiral WZNW Bloch waves satisfy a quadratic classical exchange algebra which implies the affine Kac-Moody algebra for the corresponding currents. We here obtain a direct derivation of the exchange algebra by inverting the symplectic form on the space of Bloch waves, and give a completely algorithmic construction of its generalized free field realizations that extend the classical Wakimoto realizations of the current algebra.Comment: 13 pages, LaTe

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

BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter

We summarize some recent results on the BRST analysis of physical states of 2D gravity coupled to c<=1 conformal matter and the supersymmetric generalization.Comment: 11 page

Incidence of first stroke and ethnic differences in stroke pattern in Bradford, UK: Bradford Stroke Study

Background: Information on ethnic disparities in stroke between White and Pakistani population in Europe is scarce. Bradford District has the largest proportion of Pakistani people in England; this provides a unique opportunity to study the difference in stroke between the two major ethnic groups. Aim: To determine the first-ever-stroke incidence and examine the disparities in stroke patterns between Whites and Pakistanis in Bradford. Methods: Prospective 12 months study consisting of 273,327 adults (≥18 years) residents. Stroke cases were identified by multiple overlapping approaches. Results: In the study period, 541 first-ever-strokes were recorded. The crude incidence rate was 198 per 100,000 person-years. Age adjusted-standardized rate to the World Health Organization world population of first-ever-stroke is 155 and 101 per 100,000 person-years in Pakistanis and Whites respectively. Four hundred and thirty-eight patients (81%) were Whites, 83 (15.3%) were Pakistanis, 11 (2%) were Indian and Bangladeshis, and 9 (1.7%) were of other ethnic origin. Pakistanis were significantly younger and had more obesity (p = 0.049), and diabetes mellitus (DM) (p = <0.001). They were less likely to suffer from atrial fibrillation (p = <0.001), be ex- or current smokers (p = <0.001), and drink alcohol above the recommended level (p = 0.007) compared with Whites. In comparison with Whites, higher rates of age-adjusted stroke (1.5-fold), lacunar infarction (threefold), and ischemic infarction due to large artery disease (twofold) were found in the Pakistanis. Conclusions: The incidence of first-ever-stroke is higher in the Pakistanis compared with the Whites in Bradford, UK. Etiology and vascular risk factors vary between the ethnic groups. This information should be considered when investigating stroke etiology, and when planning prevention and care provision to improve outcomes after stroke

On osp(2|2) conformal field theories

We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model.Comment: LaTex file 20 pages; Title changed and modifications mad

ZnZ_n elliptic Gaudin model with open boundaries

The $Z_n$ elliptic Gaudin model with integrable boundaries specified by generic non-diagonal K-matrices with $n+1$ free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.Comment: 21 pages, Latex fil

Painleve IV and degenerate Gaussian Unitary Ensembles

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diagonal recurrence coefficients satisfy a particular Painleve IV equation for any real multiplicity. If the multiplicity is even they are expressed in terms of the generalized Hermite polynomials, with t as the independent variable.Comment: 17 page

The N=1 triplet vertex operator superalgebras

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, 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

An Introduction to Conformal Field Theory

A comprehensive introduction to two-dimensional conformal field theory is given.Comment: 69 pages, LaTeX; references adde

Quantizing higher-spin gravity in free-field variables

We study the formulation of massless higher-spin gravity on AdS$_3$ in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for $W_N$ CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical $W_N$ charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of $W_\infty[\lambda]$. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate $W_N$ primaries, to all orders in the large central charge expansion.Comment: 31 pages + appendices. V2: typos corrected, reference adde