Ultraviolet Property of Noncommutative Wess-Zumino-Witten Model

We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The \beta-function of the U(N) noncommutative WZW model resembles that of the ordinary WZW model. The U(1) noncommutative model has also a nontrivial fixed point.Comment: 7 pages, 1 figur

Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology

In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic scenario, a matching condition between the metric perturbations in the pre-big bang phase and those in the post big-bang phase is often assumed. Various matching conditions have been considered in the literature. Nevertheless obtaining a scale invariant CMB spectrum via a concrete mechanism remains impossible. In this paper, we examine this problem from the point of view of local causality. We begin with introducing the notion of local causality and explain how it constrains the form of the matching condition. We then prove a no-go theorem: independent of the details of the matching condition, a scale invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale invariant spectrum is possible. Moreover we demonstrate that the magnitude of the spectrum is compatible with observations if the bounce is assumed to occur at an energy scale which is a few orders of magnitude below the Planckian energy scale.Comment: 15 pages, 2 figures; v3: clarifications added, changes in references, version to appear in PR

Locality, Causality and Noncommutative Geometry

We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative spacetime. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.Comment: 16 pages, LaTeX, 4 figure

Field Equations of Massless Fields in the New Interpretation of the Matrix Model

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the $B$-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.Comment: 21 page

Non-BPS Solutions of the Noncommutative CP^1 Model in 2+1 Dimensions

We find non-BPS solutions of the noncommutative CP^1 model in 2+1 dimensions. These solutions correspond to soliton anti-soliton configurations. We show that the one-soliton one-anti-soliton solution is unstable when the distance between the soliton and the anti-soliton is small. We also construct time-dependent solutions and other types of solutions.Comment: 11 pages, minor correction

Low-Energy Dynamics of Noncommutative CP^1 Solitons in 2+1 Dimensions

We investigate the low-energy dynamics of the BPS solitons of the noncommutative CP^1 model in 2+1 dimensions using the moduli space metric of the BPS solitons. We show that the dynamics of a single soliton coincides with that in the commutative model. We find that the singularity in the two-soliton moduli space, which exists in the commutative CP^1 model, disappears in the noncommutative model.We also show that the two-soliton metric has the smooth commutative limit.Comment: AMSLaTeX, 11 page

Colliding Plane Waves in String Theory

We construct colliding plane wave solutions in higher dimensional gravity theory with dilaton and higher form flux, which appears naturally in the low energy theory of string theory. Especially, the role of the junction condition in constructing the solutions is emphasized. Our results not only include the previously known CPW solutions, but also provide a wide class of new solutions that is not known in the literature before. We find that late time curvature singularity is always developed for the solutions we obtained in this paper. This supports the generalized version of Tipler's theorem in higher dimensional supergravity.Comment: latex, 25 pages, 1 figur

Hair follicle epidermal stem cells define a niche for tactile sensation

The heterogeneity and compartmentalization of stem cells is a common principle in many epithelia, and is known to function in epithelial maintenance, but its other physiological roles remain elusive. Here we show transcriptional and anatomical contributions of compartmentalized epidermal stem cells in tactile sensory unit formation in the mouse hair follicle. Epidermal stem cells in the follicle upper-bulge, where mechanosensory lanceolate complexes innervate, express a unique set of extracellular matrix (ECM) and neurogenesis-related genes. These epidermal stem cells deposit an ECM protein called EGFL6 into the collar matrix, a novel ECM that tightly ensheathes lanceolate complexes. EGFL6 is required for the proper patterning, touch responses, and αv integrin-enrichment of lanceolate complexes. By maintaining a quiescent original epidermal stem cell niche, the old bulge, epidermal stem cells provide anatomically stable follicle–lanceolate complex interfaces, irrespective of the stage of follicle regeneration cycle. Thus, compartmentalized epidermal stem cells provide a niche linking the hair follicle and the nervous system throughout the hair cycle