Non-commutative ADE geometries as holomorphic wave equations

Borrowing ideas from the relation between classical and quantum mechanics, we study a non-commutative elevation of the ADE geometries involved in building Calabi-Yau manifolds. We derive the corresponding geometric hamiltonians and the holomorphic wave equations representing these non-commutative geometries. The spectrum of the holomorphic waves is interpreted as the quantum moduli space. Quantum A_1 geometry is analyzed in some details and is found to be linked to the Whittaker differential equation.Comment: 17 pages, v2: version to be publishe

Metric Building of pp Wave Orbifold Geometries

We study strings on orbifolds of $AdS_{5}\times S^5$ by SU(2) discrete groups in the Penrose limit. We derive the degenerate metrics of pp wave of $AdS_{5}\times S^5/\Gamma$ using ordinary $ADE$ and affine \wildtilde{ADE} singularities of complex surfaces and results on ${\cal N}=4$ CFT$_4$'s. We also give explicit metric moduli depencies for abelian and non abelian orbifolds.Comment: 13 pages, no figure

Oral cancer in Libya and development of regional oral cancer registries: A review

AbstractThe aims of this paper are three-fold: (1) to summarize the current epidemiological data on oral cancer in Libya as reported in the published literature and as compared to other national oral cancer rates in the region; (2) to present both the history of the early development, and future goals, of population-based oral cancer tumor registries in Libya as they partner with the more established regional and international population-based cancer tumor registries; and, (3) to offer recommendations that will likely be required in the near future if these nascent, population-based Libyan oral cancer registries are to establish themselves as on-going registries for describing the oral cancer disease patterns and risk factors in Libya as well as for prevention and treatment. This comprehensive literature review revealed that the current baseline incidence of oral cancer in Libya is similar to those of other North Africa countries and China, but is relatively low compared to the United Kingdom, the United States, and India. The recently established Libyan National Cancer Registry Program, initiated in 2007, while envisioning five cooperating regional cancer registries, continues to operate at a relatively suboptimal level. Lack of adequate levels of national funding continue to plague its development…and the accompanying quality of service that could be provided to the Libyan people

Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories

Starting from the $\mathcal{N}=2$ SYM$_{4}$ quiver theory living on wrapped $$ branes around $S_{i}^{2}$ spheres of deformed ADE fibered Calabi-Yau threefolds (CY3) and considering deformations using \textit{% massive} vector multiplets, we explicitly build a new class of $\mathcal{N}$ quiver gauge theories. In these models, the quiver gauge group $\prod_{i}U(N_{i})$ is spontaneously broken down to $$ and Kahler deformations are shown to be given by the real part of the integral $(2,1)$ form of CY3. We also give the superfield correspondence between the $\mathcal{N}=1$ quiver gauge models derived here and those constructed in hep-th/0108120 using complex deformations. Others aspects of these two dual $\mathcal{N}=1$ supersymmetric field theories are discussed.Comment: 12 pages, 1 figur

String compactifications on Calabi-Yau stacks

In this paper we study string compactifications on Deligne-Mumford stacks. The basic idea is that all such stacks have presentations to which one can associate gauged sigma models, where the group gauged need be neither finite nor effectively-acting. Such presentations are not unique, and lead to physically distinct gauged sigma models; stacks classify universality classes of gauged sigma models, not gauged sigma models themselves. We begin by defining and justifying a notion of ``Calabi-Yau stack,'' recall how one defines sigma models on (presentations of) stacks, and calculate of physical properties of such sigma models, such as closed and open string spectra. We describe how the boundary states in the open string B model on a Calabi-Yau stack are counted by derived categories of coherent sheaves on the stack. Along the way, we describe numerous tests that IR physics is presentation-independent, justifying the claim that stacks classify universality classes. String orbifolds are one special case of these compactifications, a subject which has proven controversial in the past; however we resolve the objections to this description of which we are aware. In particular, we discuss the apparent mismatch between stack moduli and physical moduli, and how that discrepancy is resolved.Comment: 85 pages, LaTeX; v2: typos fixe

Mean Field Theory of Spherical Gravitating Systems

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems confined in a finite domain consisting of either point masses, or rotating mass shells of different dimension. We establish a direct connection between the spherically symmetric equilibrium states of a self-gravitating point mass system and a shell model of dimension 3. We construct the equilibrium density functions by maximizing the entropy subject to the usual constraints of normalization and energy, but we also take into account the constraint on the sum of the squares of the individual angular momenta, which is also an integral of motion for these symmetric systems. Two new statistical ensembles are introduced which incorporate the additional constraint. They are used to investigate the possible occurrence of a phase transition as the defining parameters for each ensemble are altered

Toric Varieties with NC Toric Actions: NC Type IIA Geometry

Extending the usual $\mathbf{C}^{\ast r}$ actions of toric manifolds by allowing asymmetries between the various $\mathbf{C}^{\ast}$ factors, we build a class of non commutative (NC) toric varieties $\mathcal{V}$. We construct NC complex $d$ dimension Calabi-Yau manifolds embedded in $\mathcal{V}_{d+1}^{(nc)}$ by using the algebraic geometry method. Realizations of NC $\mathbf{C}^{\ast r}$ toric group are given in presence and absence of quantum symmetries and for both cases of discrete or continuous spectrums. We also derive the constraint eqs for NC Calabi-Yau backgrounds $\mathcal{M}_{d}^{nc}$ embedded in $\mathcal{V}_{d+1}^{nc}$ and work out their solutions. The latters depend on the Calabi-Yau condition $\sum_{i}q_{i}^{a}=0$, $q_{i}^{a}$ being the charges of $\mathbf{C}^{\ast r}$% ; but also on the toric data ${q_{i}^{a},\nu_{i}^{A};p_{I}^{\alpha},\nu _{iA}^{\ast}}$ of the polygons associated to $\mathcal{V}$. Moreover, we study fractional $D$ branes at singularities and show that, due to the complete reducibility property of $\mathbf{C}^{\ast r}$ group representations, there is an infinite number of fractional $D$ branes. We also give the generalized Berenstein and Leigh quiver diagrams for discrete and continuous $\mathbf{C}^{\ast r}$ representation spectrums. An illustrating example is presented.Comment: 25 pages, no figure

Constrained simulations of the Local Group: on the radial distribution of substructures

We examine the properties of satellites found in high resolution simulations of the local group. We use constrained simulations designed to reproduce the main dynamical features that characterize the local neighborhood, i.e. within tens of Mpc around the Local Group (LG). Specifically, a LG-like object is found located within the 'correct' dynamical environment and consisting of three main objects which are associated with the Milky Way, M31 and M33. By running two simulations of this LG from identical initial conditions - one with and one without baryons modeled hydrodynamically - we can quantify the effect of gas physics on the $z=0$ population of subhaloes in an environment similar to our own. We find that above a certain mass cut, $M_{\rm sub} > 2\times10^{8}h^{-1} M_{\odot}$ subhaloes in hydrodynamic simulations are more radially concentrated than those in simulations with out gas. This is caused by the collapse of baryons into stars that typically sit in the central regions of subhaloes, making them denser. The increased central density of such a subhalo, results in less mass loss due to tidal stripping than the same subhalo simulated with only dark matter. The increased mass in hydrodynamic subhaloes with respect to dark matter ones, causes dynamical friction to be more effective, dragging the subhalo towards the centre of the host. This results in these subhaloes being effectively more radially concentrated then their dark matter counterparts.Comment: 12 pages, 9 figure

How supernova feedback turns dark matter cusps into cores

We propose and successfully test against new cosmological simulations a novel analytical description of the physical processes associated with the origin of cored dark matter density profiles. In the simulations, the potential in the central kiloparsec changes on sub-dynamical timescales over the redshift interval 4 > z > 2 as repeated, energetic feedback generates large underdense bubbles of expanding gas from centrally-concentrated bursts of star formation. The model demonstrates how fluctuations in the central potential irreversibly transfer energy into collisionless particles, thus generating a dark matter core. A supply of gas undergoing collapse and rapid expansion is therefore the essential ingredient. The framework, based on a novel impulsive approximation, breaks with the reliance on adiabatic approximations which are inappropriate in the rapidly-changing limit. It shows that both outflows and galactic fountains can give rise to cusp-flattening, even when only a few per cent of the baryons form stars. Dwarf galaxies maintain their core to the present time. The model suggests that constant density dark matter cores will be generated in systems of a wide mass range if central starbursts or AGN phases are sufficiently frequent and energetic.Comment: 9 pages, 6 figures, accepted by MNRAS. No change in results. Expanded discussion and more reference