The spectral geometry of the canonical Riemannian submersion of a compact Lie Group

Let G be a compact connected Lie group which is equipped with a bi-invariant Riemannian metric. Let m(x,y)=xy be the multiplication operator. We show the associated fibration m mapping GxG to G is a Riemannian submersion with totally geodesic fibers and we study the spectral geometry of this submersion. We show the pull back of eigenforms on the base have finite Fourier series on the total space and we give examples where arbitrarily many Fourier coefficients can be non-zero. We give necessary and sufficient conditions that the pull back of a form on the base is harmonic on the total space

Total daily energy expenditure in black and white, lean and obese South African women.

Background/Objectives:In South Africa (SA), the prevalence of obesity in women is 56%, with black women being most at risk (62%). Studies in the United States have demonstrated ethnic differences in resting (REE) and total daily energy expenditure (TDEE) between African American (AA) and their white counterparts. We investigated whether differences in EE exist in black and white SA women, explaining, in part, the ethnic obesity prevalence differences.Subjects/Methods:We measured REE, TDEE and physical activity EE (PAEE) in lean (BMI 30 kg m(-2)) SA women (N=44, 30+/-6 year). REE, TDEE, PAEE and total awake EE were measured during a 21 h stay in a respiration chamber.Results:Black and white subjects within obese and lean groups were not significantly different for age, mass, BMI and % body fat. However, fat-free mass (kg FFM) was consistently lower in the black women (P<0.01) in both weight groups. After adjusting EE measurements for differences in FFM, REE was not significantly different for either body weight or ethnicity, although 24 h TDEE (kJ) was significantly greater in the obese women (P<0.01) and white women (P<0.05). Total awake non-PAEE was not significantly different for either groups, while total awake time was only significantly lower for the lean groups (P<0.01). Total PAEE (kJ min(-1)) was significantly lower in the lean (P<0.001) and black groups (P<0.01).Conclusions:In this sample of matched, lean and obese, black and white SA women, differences in TDEE were largely explained by ethnic differences in PAEE, and were not as a result of ethnic differences in REE.European Journal of Clinical Nutrition advance online publication, 13 February 2008; doi:10.1038/ejcn.2008.8

Constraining Maximally Supersymmetric Membrane Actions

We study the recent construction of maximally supersymmetric field theory Lagrangians in three spacetime dimensions that are based on algebras with a triple product. Assuming that the algebra has a positive definite metric compatible with the triple product, we prove that the only non-trivial examples are either the well known case based on a four dimensional algebra or direct sums thereof.Comment: 11 pages, very minor changes. Reference added. Version to be published in JHE

Intersection rules, dynamics and symmetries

We consider theories containing gravity, at most one dilaton and form field strengths. We show that the existence of particular BPS solutions of intersecting extremal closed branes select the theories, which upon dimensional reduction to three dimensions possess a simple simply laced Lie group symmetry G. Furthermore these theories can be fully reconstructed from the dynamics of such branes and of their openings. Amongst such theories are the effective actions of the bosonic sector of M-theory and of the bosonic string. The BPS intersecting brane solutions form representations of a subgroup of the group of Weyl reflections and outer automorphisms of the triple Kac-Moody extension G+++ of the G algebra, which cannot be embedded in the overextended Kac-Moody subalgebra G++ characterising the cosmological Kasner solutions.Comment: Latex 30 pages, 3 figure

Proposal for the Open String Tachyon Effective Action in the Linear Dilaton Background

In this paper we propose tachyon effective actions for unstable D-branes in superstring and bosonic string theories in the presence of the linear dilaton background.Comment: 18 page

Noncommutative geometry, Quantum effects and DBI-scaling in the collapse of D0-D2 bound states

We study fluctuations of time-dependent fuzzy two-sphere solutions of the non-abelian DBI action of D0-branes, describing a bound state of a spherical D2-brane with N D0-branes. The quadratic action for small fluctuations is shown to be identical to that obtained from the dual abelian D2-brane DBI action, using the non-commutative geometry of the fuzzy two-sphere. For some of the fields, the linearized equations take the form of solvable Lam\'e equations. We define a large-N DBI-scaling limit, with vanishing string coupling and string length, and where the gauge theory coupling remains finite. In this limit, the non-linearities of the DBI action survive in both the classical and the quantum context, while massive open string modes and closed strings decouple. We describe a critical radius where strong gauge coupling effects become important. The size of the bound quantum ground state of multiple D0-branes makes an intriguing appearance as the radius of the fuzzy sphere, where the maximal angular momentum quanta become strongly coupled.Comment: 34 pages, Latex; v2: Minor correction in conformal transformation of couplings, references adde

Andreev reflections in the pseudogap state of cuprate supercondcutors

We propose that, if the pseudogap state in the cuprate superconductors can be described in terms of the phase-incoherent preformed pairs, there should exist Andreev reflection from these pairs even above the superconducting transition temperature, $T_c$. After giving qualitative arguments for this effect, we present more quantitative calculations based on the Bogoliubov--de Gennes equation. Experimental observations of the effects of Andreev reflections above $T_c$---such as an enhanced tunneling conductance below the gap along the copper oxide plane---could provide unambiguous evidence for the preformed pairs in the pseudogap state.Comment: 5 pages, 1 figur

Tachyon Kinks on Unstable Dp-branes

In the context of tachyon effective theory coupled to Born-Infeld electromagnetic fields, we obtain all possible singularity-free static flat configurations of codimension one on unstable Dp-branes. Computed tension and string charge density suggest that the obtained kinks are D(p-1) or D(p-1)F1-branes.Comment: 22pages, LaTeX2e, 7figure

Correlations of structural, magnetic, and dielectric properties of undoped and doped CaCu3Ti4O12

The present work reports synthesis, as well as a detailed and careful characterization of structural, magnetic, and dielectric properties of differently tempered undoped and doped CaCu3Ti4O12 (CCTO) ceramics. For this purpose, neutron and x-ray powder diffraction, SQUID measurements, and dielectric spectroscopy have been performed. Mn-, Fe-, and Ni-doped CCTO ceramics were investigated in great detail to document the influence of low-level doping with 3d metals on the antiferromagnetic structure and dielectric properties. In the light of possible magnetoelectric coupling in these doped ceramics, the dielectric measurements were also carried out in external magnetic fields up to 7 T, showing a minor but significant dependence of the dielectric constant on the applied magnetic field. Undoped CCTO is well-known for its colossal dielectric constant in a broad frequency and temperature range. With the present extended characterization of doped as well as undoped CCTO, we want to address the question why doping with only 1% Mn or 0.5% Fe decreases the room-temperature dielectric constant of CCTO by a factor of ~100 with a concomitant reduction of the conductivity, whereas 0.5% Ni doping changes the dielectric properties only slightly. In addition, diffraction experiments and magnetic investigations were undertaken to check for possible correlations of the magnitude of the colossal dielectric constants with structural details or with magnetic properties like the magnetic ordering, the Curie-Weiss temperatures, or the paramagnetic moment. It is revealed, that while the magnetic ordering temperature and the effective moment of all investigated CCTO ceramics are rather similar, there is a dramatic influence of doping and tempering time on the Curie-Weiss constant.Comment: 10 pages, 11 figure

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure