Maximal supersymmetry and exceptional groups

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself where we describe the N = 8 Supergravity in the light-cone formalism. We show how the Cremmer-Julia E7(7) non-linear symmetry is implemented and how the full supermultiplet is a representation of the E7(7) symmetry. I also show how the E7(7) symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.Comment: Proceedings of Conference in Honour of Murray Gell-Mann's 80th Birthda

Oxidizing SuperYang-Mills from (N=4,d=4) to (N=1,d=10)

We introduce superspace generalizations of the transverse derivatives to rewrite the four-dimensional N=4 Yang-Mills theory into the fully ten-dimensional N=1 Yang-Mills in light-cone form. The explicit SuperPoincare algebra is constructed and invariance of the ten-dimensional action is proved.Comment: 15 page

KCrF_3: Electronic Structure, Magnetic and Orbital Ordering from First Principles

The electronic, magnetic and orbital structures of KCrF_3 are determined in all its recently identified crystallographic phases (cubic, tetragonal, and monoclinic) with a set of {\it ab initio} LSDA and LSDA+U calculations. The high-temperature undistorted cubic phase is metallic within the LSDA, but at the LSDA+U level it is a Mott insulator with a gap of 1.72 eV. The tetragonal and monoclinic phases of KCrF_3 exhibit cooperative Jahn-Teller distortions concomitant with staggered 3x^2-r^2/3y^2-r^2 orbital order. We find that the energy gain due to the Jahn-Teller distortion is 82/104 meV per chromium ion in the tetragonal/monoclinic phase, respectively. These phases show A-type magnetic ordering and have a bandgap of 2.48 eV. In this Mott insulating state KCrF_3 has a substantial conduction bandwidth of 2.1 eV, leading to the possibility for the kinetic energy of charge carriers in electron- or hole-doped derivatives of KCrF_3 to overcome the polaron localization at low temperatures, in analogy with the situation encountered in the colossal magnetoresistive manganites.Comment: 7 pages, 11 figure

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

A relativistic treatment of pion wave functions in the annihilation antiproton-proton -> pi^-pi^+

Quark model intrinsic wave functions of highly energetic pions in the reaction \bar pp->\pi^-\pi^+ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology and the annihilated quark-antiquark pairs are in 3P_0 and 3S_1 states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.Comment: 10 pages in revtex format, 3 figure

Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes

An analytic understanding of the geodesic structure around non-Kerr spacetimes will result in a powerful tool that could make the mapping of spacetime around massive quiescent compact objects possible. To this end, I present an analytic closed form expression for the components of a the fourth order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is as yet unclear what subset of SAV spacetimes admit this solution. The solution is written in terms of an integral expression involving the metric functions and two specific Greens functions. A second integral expression has to vanish in order for the solution to be exact. In the event that the second integral does not vanish it is likely that the best fourth order approximation to the invariant has been found. This solution can be viewed as a generalized Carter constant providing an explicit expression for the fourth invariant, in addition to the energy, azimuthal angular momentum and rest mass, associated with geodesic motion in SAV spacetimes, be it exact or approximate. I further comment on the application of this result for the founding of a general algorithm for mapping the spacetime around compact objects using gravitational wave observatories.Comment: 5 Page

Photoassociation spectra and the validity of the dipole approximation for weakly bound dimers

Photoassociation (PA) of ultracold metastable helium to the 2s2p manifold is theoretically investigated using a non-perturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [Cocks and Whittingham, Phys. Rev. A 80, 023417 (2009)] that makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion or not of the approximation does not affect the resonance positions or widths, however significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernable. Couplings not satisfying the dipole selection rule |J-1| <= J' <= |J+1| do not lead to observable resonances.Comment: 5 pages, 2 figures; Minor textual revision

Screening and characterization of Lactobacillus strains producing large amounts of exopolysaccharides

A total of 182 Lactobacillus strains were screened for production of extracellular polysaccharides (EPS) by a new method: growth in liquid media with high sugar concentrations. Sixty EPS-positive strains were identified; 17 strains produced more than 100 mg/l soluble EPS. Sucrose was an excellent substrate for abundant EPS synthesis. The ability to produce glucans appears to be widespread in the genus Lactobacillus. The monosaccharide composition of EPS produced by Lactobacillus reuteri strain LB 121 varied with the growth conditions (solid compared to liquid medium) and the sugar substrates (sucrose or raffinose) supplied in the medium. Strain LB 121 produced both a glucan and a fructan on sucrose, but only a fructan on raffinose. This is the first report of fructan production by a Lactobacillus species. EPS production increased with increasing sucrose concentrations and involved extracellular sucrase-type enzymes.

Twin building lattices do not have asymptotic cut-points

We show that twin building lattices have linear divergence, which implies that all asymptotic cones are without cut-points.Comment: 7 page

On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page