The Kazhdan-Lusztig conjecture for W-algebras

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine Kac-Moody algebras and in a similar fashion W modules from KM modules. Assuming certain properties of this functor, the W characters are subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The result can be formulated in terms of a double coset of the Weyl group of the KM algebra: the Hasse diagrams give the embedding diagrams of the Verma modules and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.Comment: uuencoded file, 29 pages latex, 5 figure

Spontaneous Vortex Lattices in Quasi 2D Dipolar Spinor Condensates

Motivated by recent experiments\cite{BA}\cite{BB}, we study quasi 2D ferromagnetic condensates with various aspect ratios. We find that in zero magnetic field, dipolar energy generates a local energy minimum with all the spins lie in the 2D plane forming a row of {\em circular} spin textures with {\em alternating} orientation, corresponding to a packing of vortices of {\em identical} vorticity in different spin components. In a large magnetic field, the system can fall into a long lived dynamical state consisting of an array of elliptic and hyperbolic Mermin-Ho spin textures, while the true equilibrium is an uniaxial spin density wave with a single wave-vector along the magnetic field, and a wavelength similar to the characteristic length of the long lived vortex array state.Comment: 4 pages, 6 figure

A note on entropic force and brane cosmology

Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can be derived from this holographic scenario.Comment: 5 pages, no figures;references adde

Induced magnetization in La0.7_{0.7}Sr0.3_{0.3}MnO3_3/BiFeO3_3 superlattices

Using polarized neutron reflectometry (PNR), we observe an induced magnetization of 75$\pm$ 25 kA/m at 10 K in a La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO)/BiFeO$_3$ superlattice extending from the interface through several atomic layers of the BiFeO$_3$ (BFO). The induced magnetization in BFO is explained by density functional theory, where the size of bandgap of BFO plays an important role. Considering a classical exchange field between the LSMO and BFO layers, we further show that magnetization is expected to extend throughout the BFO, which provides a theoretical explanation for the results of the neutron scattering experiment.Comment: 5 pages, 4 figures, with Supplemental Materials. To appear in Physical Review Letter

Conditional over-expression of PITX1 causes skeletal muscle dystrophy in mice

Paired-like homeodomain transcription factor 1 (PITX1) was specifically up-regulated in patients with facioscapulohumeral muscular dystrophy (FSHD) by comparing the genome-wide mRNA expression profiles of 12 neuromuscular disorders. In addition, it is the only known direct transcriptional target of the double homeobox protein 4 (DUX4) of which aberrant expression has been shown to be the cause of FSHD. To test the hypothesis that up-regulation of PITX1 contributes to the skeletal muscle atrophy seen in patients with FSHD, we generated a tet-repressible muscle-specific Pitx1 transgenic mouse model in which expression of PITX1 in skeletal muscle can be controlled by oral administration of doxycycline. After PITX1 was over-expressed in the skeletal muscle for 5 weeks, the mice exhibited significant loss of body weight and muscle mass, decreased muscle strength, and reduction of muscle fiber diameters. Among the muscles examined, the tibialis anterior, gastrocnemius, quadricep, bicep, tricep and deltoid showed significant reduction of muscle mass, while the soleus, masseter and diaphragm muscles were not affected. The most prominent pathological change was the development of atrophic muscle fibers with mild necrosis and inflammatory infiltration. The affected myofibers stained heavily with NADH-TR with the strongest staining in angular-shaped atrophic fibers. Some of the atrophic fibers were also positive for embryonic myosin heavy chain using immunohistochemistry. Immunoblotting showed that the p53 was up-regulated in the muscles over-expressing PITX1. The results suggest that the up-regulation of PITX1 followed by activation of p53-dependent pathways may play a major role in the muscle atrophy developed in the mouse model

Logarithmic corrections to black hole and black ring entropy in tunneling approach

The tunneling approach beyond semiclassical approximation has been used to calculate the corrected Hawking temperature and entropy for various black holes and FRW universe model. We examine their derivations, and prove that the quantity $H$ in the corrected temperature is the explicit function of the only free parameter $\mathcal{A}$ (which is an auxiliary parameter defined by $\mathcal{A}=\hbar S_{BH}$). Our analysis improves previous calculations, and indicates that the leading order logarithmic correction to entropy is a natural result of the corrected temperature and the first law of thermodynamics. Additionally, we apply the tunneling approach beyond semiclassical approximation to neutral black rings. Based on the analysis, we show that the entropy of neutral black rings also has a logarithmic leading order correction.Comment: 13 pages, rewritte