`Hidden' Symmetries of Higher Dimensional Rotating Black Holes

We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same `hidden' symmetry as the 4-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.Comment: 4 pages, slightly extended introductio

Melting Pattern of Diquark Condensates in Quark Matter

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. Effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) -> a ``dSC'' phase (ud and ds pairings) -> an isoscalar pairing phase (ud pairing) -> a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are massive as in the mCFL phase, three out of nine quark quasiparticles are gapless.Comment: minor changes in the text, fig.2 modifie

Intrinsic electric field effects on few-particle interactions in coupled GaN quantum dots

We study the multi-exciton optical spectrum of vertically coupled GaN/AlN quantum dots with a realistic three-dimensional direct-diagonalization approach for the description of few-particle Coulomb-correlated states. We present a detailed analysis of the fundamental properties of few-particle/exciton interactions peculiar of nitride materials. The giant intrinsic electric fields and the high electron/hole effective masses give rise to different effects compared to GaAs-based quantum dots: intrinsic exciton-exciton coupling, non-molecular character of coupled dot exciton wavefunction, strong dependence of the oscillator strength on the dot height, large ground state energy shift for dots separated by different barriers. Some of these effects make GaN/AlN quantum dots interesting candidates in quantum information processing.Comment: 23 pages, 8 figures, 1 tabl

Color Superconductivity from Supersymmetry

A supersymmetric composite model of color superconductivity is proposed. Quarks and diquarks are dynamically generated as composite fields by a newly introduced strong gauge dynamics. It is shown that the condensation of the scalar component of the diquark supermultiplet occurs when the chemical potential becomes larger than some critical value. We believe that the model well captures aspects of the diquark condensate behavior and helps our understanding of the diquark dynamics in real QCD. The results obtained here might be useful when we consider a theory composed of quarks and diquarks.Comment: 4 pages, 2 figures, An error in Eq.(10) correcte

Conformal Yano-Killing tensor for the Kerr metric and conserved quantities

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed.Comment: 29 page

Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kaehler metrics into Kaehler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kaehler metrics is shown to be exactly the class of Kaehler metrics whose potential function is only a function of the distance from the origin in complex Euclidean space. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kaehler structure, which is of quasi-constant holomorphic sectional curvatures.Comment: 36 page