Interplay of Mott Transition and Ferromagnetism in the Orbitally Degenerate Hubbard Model

A slave boson representation for the degenerate Hubbard model is introduced. The location of the metal to insulator transition that occurs at commensurate densities is shown to depend weakly on the band degeneracy M. The relative weights of the Hubbard sub-bands depend strongly on M, as well as the magnetic properties. It is also shown that a sizable Hund's rule coupling is required in order to have a ferromagnetic instability appearing. The metal to insulator transition driven by an increase in temperature is a strong function of it.Comment: 5 pages, revtex, 5 postscript figures, submitted to Phys. Rev.

Supersymmetric IIB Solutions with Schr\"{o}dinger Symmetry

We find a class of non-relativistic supersymmetric solutions of IIB supergravity with non-trivial B-field that have dynamical exponent n=2 and are invariant under the Schrodinger group. For a general Sasaki-Einstein internal manifold with U(1)^3 isometry, the solutions have two real supercharges. When the internal manifold is S^5, the number of supercharges can be four. We also find a large class of non-relativistic scale invariant type IIB solutions with dynamical exponents different from two. The explicit solutions and the values of the dynamical exponents are determined by vector eigenfunctions and eigenvalues of the Laplacian on an Einstein manifold.Comment: 28 pages, LaTe

Obstructions to the Existence of Sasaki-Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R-charge of a gauge invariant chiral primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde

Freezing in the Sun

When the air is very cold, water at the surface of the ocean freezes, forming sea ice. Parts of the Arctic Ocean are covered by sea ice during the entire year. Often, snow falls onto the sea ice. Despite the cold, many plants and animals can live in the Arctic Ocean, some in the water, and some even in the sea ice. Particularly, algae can live in small bubbles in the sea ice. Like other plants, algae need energy to grow. This energy comes from food and sunlight. But how can the sunlight reach these little algae living inside the sea ice? From the sun, the light must pass through the atmosphere, the snow, and finally the sea ice itself. In this article, we describe how ice algae can live in this special environment and we explain what influences how much light reaches the algae to make them grow

Phase Separation Based on U(1) Slave-boson Functional Integral Approach to the t-J Model

We investigate the phase diagram of phase separation for the hole-doped two dimensional system of antiferromagnetically correlated electrons based on the U(1) slave-boson functional integral approach to the t-J model. We show that the phase separation occurs for all values of J/t, that is, whether $0 < J/t < 1$ or $J/t \geq 1$ with J, the Heisenberg coupling constant and t, the hopping strength. This is consistent with other numerical studies of hole-doped two dimensional antiferromagnets. The phase separation in the physically interesting J region, $0 < J/t \lesssim 0.4$ is examined by introducing hole-hole (holon-holon) repulsive interaction. We find from this study that with high repulsive interaction between holes the phase separation boundary tends to remain robust in this low $J$ region, while in the high J region, J/t > 0.4, the phase separation boundary tends to disappear.Comment: 4 pages, 2 figures, submitted to Phys. Rev.

Two-species percolation and Scaling theory of the metal-insulator transition in two dimensions

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two dimensions [1]. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the ``metallic'' point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model. Moreover, details such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs. parallel magnetic are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction. It is also shown that the resistance on the ``metallic'' side can decrease with decreasing temperature by an arbitrary factor in the degenerate regime ($T\lesssim E_F$).Comment: 8 pages, 8 figure

First Stars. I. Evolution without mass loss

The first generation of stars was formed from primordial gas. Numerical simulations suggest that the first stars were predominantly very massive, with typical masses M > 100 Mo. These stars were responsible for the reionization of the universe, the initial enrichment of the intergalactic medium with heavy elements, and other cosmological consequences. In this work, we study the structure of Zero Age Main Sequence stars for a wide mass and metallicity range and the evolution of 100, 150, 200, 250 and 300 Mo galactic and pregalactic Pop III very massive stars without mass loss, with metallicity Z=10E-6 and 10E-9, respectively. Using a stellar evolution code, a system of 10 equations together with boundary conditions are solved simultaneously. For the change of chemical composition, which determines the evolution of a star, a diffusion treatment for convection and semiconvection is used. A set of 30 nuclear reactions are solved simultaneously with the stellar structure and evolution equations. Several results on the main sequence, and during the hydrogen and helium burning phases, are described. Low metallicity massive stars are hotter and more compact and luminous than their metal enriched counterparts. Due to their high temperatures, pregalactic stars activate sooner the triple alpha reaction self-producing their own heavy elements. Both galactic and pregalactic stars are radiation pressure dominated and evolve below the Eddington luminosity limit with short lifetimes. The physical characteristics of the first stars have an important influence in predictions of the ionizing photon yields from the first luminous objects; also they develop large convective cores with important helium core masses which are important for explosion calculations.Comment: 17 pages, 24 figures, 2 table

Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory

We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions and we determine all four-dimensional gauge theories resulting from the generalized dimensional reduction a la Forgacs-Manton over coset spaces, followed by a subsequent application of the Wilson flux spontaneous symmetry breaking mechanism. Our investigation is constrained only by the requirements that (i) the dimensional reduction leads to the potentially phenomenologically interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and (ii) the Wilson flux mechanism makes use only of the freely acting discrete symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty, ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C

Magnetic polarons in weakly doped high-Tc superconductors

We consider a spin Hamiltonian describing $d$-$d$ exchange interactions between localized spins $d$ of a finite antiferromagnet as well as $p$-$d$ interactions between a conducting hole ($p$) and localized spins. The spin Hamiltonian is solved numerically with use of Lanczos method of diagonalization. We conclude that $p$-$d$ exchange interaction leads to localization of magnetic polarons. Quantum fluctuations of the antiferromagnet strengthen this effect and make the formation of polarons localized in one site possible even for weak $p$-$d$ coupling. Total energy calculations, including the kinetic energy, do not change essentially the phase diagram of magnetic polarons formation. For parameters reasonable for high-$T_c$ superconductors either a polaron localized on one lattice cell or a small ferron can form. For reasonable values of the dielectric function and $p$-$d$ coupling, the contributions of magnetic and phonon terms in the formation of a polaron in weakly doped high-$T_c$ materials are comparable.Comment: revised, revtex-4, 12 pages 8 eps figure

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc