Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

Electron Spin Dynamics of the Superconductor CaC6 probed by ESR

Conduction Electron Spin Resonance (CESR) was measured on a thick slab of CaC6 in the normal and superconducting state. A surprising increase of the CESR intensity below Tc can not be explained by the theoretically predicted change in spin susceptibility. It is interpreted as a vortex enhanced increase of the effective skin depth. Non-linear microwave absorption measurements in the superconducting state describe CaC6 as an anisotropic BCS superconductor. The study of the spin dynamics in the superconducting state and the discovery of the vortex enhanced increase of the skin depth poses a challenge to theory to provide a comprehensive description of the observed phenomena. CESR data in the normal state characterize CaC6 as a three-dimensional (3D) metal. The analysis suggests that the scattering of conduction electrons is dominated by impurities and supports the description of superconductivity in the dirty limit.Comment: 4 pages, 3 figure

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H.Comment: v2: 14 pages, minor correction

Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies

3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e. these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes. Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors

The Conformal Manifold of Chern-Simons Matter Theories

We determine perturbatively the conformal manifold of N=2 Chern-Simons matter theories with the aim of checking in the three dimensional case the general prescription based on global symmetry breaking, recently introduced. We discuss in details few remarkable cases like the N=6 ABJM theory and its less supersymmetric generalizations with/without flavors. In all cases we find perfect agreement with the predictions of global symmetry breaking prescription.Comment: 1+17 pages, 1 figure, references adde

Virtual Top-Quark Effects on the H->bb-bar Decay at Next-to-Leading Order in QCD

By means of a heavy-top-quark effective Lagrangian, we calculate the three-loop corrections of O(alpha_s^2 G_F M_t^2) to the H->bb-bar partial decay width of the standard-model Higgs boson with intermediate mass M_H<<2M_t. We take advantage of a soft-Higgs theorem to construct the relevant coefficient functions. We present our result both in the MS-bar and on-shell schemes of mass renormalization. The MS-bar formulation turns out to be favourable with regard to the convergence behaviour. We also test a recent idea concerning the naive non-abelianization of QCD.Comment: 8 pages (Latex), 5 figures (Postscript

Searching for Anomalous Weak Couplings of Heavy Flavors at the SLC and LEP

The existence of anomalous electric($\tilde \kappa$) and/or magnetic($\kappa$) dipole moment couplings between the heavy flavor fermions ($c,b,\tau$) and the $Z$ boson can cause significant shifts in the values of several electroweak observables currently being probed at both the SLC and LEP. Using the good agreement between existing data and the predictions of the Standard Model we obtain strict bounds on the possible strength of these new interactions for all of the heavy flavors. The decay $Z\rightarrow b\bar b$, however, provides some possible hint of new physics. The corresponding anomalous couplings of $\tau$'s to photons is briefly examined.Comment: 21 pages, 14 figs(available on request), LaTex, SLAC-PUB-667

A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Crystal Structure of the Sodium Cobaltate Deuterate Superconductor NaxCoO2o4xD2O (x=1/3)

Neutron and x-ray powder diffraction have been used to investigate the crystal structures of a sample of the newly-discovered superconducting sodium cobaltate deuterate compound with composition Na0.31(3)CoO2o1.25(2)D2O and its anhydrous parent compound Na0.61(1)CoO2. The deuterate superconducting compound is formed by coordinating four D2O molecules (two above and two below) to each Na ion in a way that gives Na-O distances nearly equal to those in the parent compound. One deuteron of the D2O molecule is hydrogen bonded to an oxygen atom in the CoO2 plane and the oxygen atom and the second deuteron of each D2O molecule lie approximately in a plane between the Na layer and the CoO2 layers. This coordination of Na by four D2O molecules leads to ordering of the Na ions and D2O molecules. The sample studied here, which has Tc=4.5 K, has a refined composition of Na0.31(3)CoO2o1.25(2)D2O, in agreement with the expected 1:4 ratio of Na to D2O. These results show that the optimal superconducting composition should be viewed as a specific hydrated compound, not a solid solution of Na and D2O (H2O) in NaxCoO2oyD2O. Studies of physical properties vs. Na or D2O composition should be viewed with caution until it is verified that the compound remains in the same phase over the composition range of the study.Comment: 22 pages, 8 figure