Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models

"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs are known as "Adinkras"). We further prove the existence of "entangled" linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3,8,5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as chirality and coloring can discriminate different supermultiplets. The tools used in our classification include, among others, the notion of field content, connectivity symbol, commuting group, node choice group and so on.Comment: 20 pages, 5 figures. Two references adde

Stable Existence of Phase IV inside Phase II under Pressure in Ce0.8_{0.8}La0.2_{0.2}B6_{6}

We investigate the pressure effect of the electrical resistivity and magnetization of Ce$_{0.8}$La$_{0.2}$B$_{6}$. The situation in which phase IV stably exists inside phase II at H=0 T could be realized by applying a pressure above $P\sim 1.1$ GPa. This originates from the fact that the stability of phase II under pressure is larger than those of phases IV and III. The results seem to be difficult to reproduce by taking the four interactions of $\Gamma_{\mathrm{5u}}$-type AFO, $O_{xy}$-type AFQ, $T_{xyz}$-type AFO, and AF exchange into account within a mean-field calculation framework.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn. 79 (2010) No.

On General Off-Shell Representations of Worldline (1D) Supersymmetry

Every finite-dimensional unitary representation of the N-extended worldline supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets that are identifiable with representations of the Clifford algebra. The data specifying this procedure is a sequence of subspaces of the direct sum of Adinkras, which then opens an avenue for classification of the continuum of so constructed off-shell supermultiplets.Comment: 21 pages, 5 illustrations; references update

Evidence for short-range antiferromagnetic fluctuations in Kondo-insulating YbB12

The spin dynamics of mixed-valence YbB12 has been studied by inelastic neutron scattering on a high-quality single crystal. In the Kondo-insulating regime realized at low temperature, the spectra exhibit a spin-gap structure with two sharp, dispersive, in-gap excitations at E = 14.5 and approximately 20 meV. The lower mode is shown to be associated with short-range correlations near the antiferromagnetic wave vector q0 = (1/2, 1/2, 1/2). Its properties are in overall agreement with those expected for a "spin exciton'' branch in an indirect hybridization gap semiconductor.Comment: 4 pages, 4 figures ; submitted to Physical Review Letter

Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.Comment: 13 Figure

An application of cubical cohomology to Adinkras and supersymmetry representations

An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincaré algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds