Locally Localized Gravity Models in Higher Dimensions

We explore the possibility of generalizing the locally localized gravity model in five space-time dimensions to arbitrary higher dimensions. In a space-time with negative cosmological constant, there are essentially two kinds of higher-dimensional cousins which not only take an analytic form but also are free from the naked curvature singularity in a whole bulk space-time. One cousin is a trivial extension of five-dimensional model, while the other one is in essence in higher dimensions. One interesting observation is that in the latter model, only anti-de Sitter ($AdS_p$) brane is physically meaningful whereas de Sitter ($dS_p$) and Minkowski ($M_p$) branes are dismissed. Moreover, for $AdS_p$ brane in the latter model, we study the property of localization of various bulk fields on a single brane. In particular, it is shown that the presence of the brane cosmological constant enables bulk gauge field and massless fermions to confine to the brane only by a gravitational interaction. We find a novel relation between mass of brane gauge field and the brane cosmological constant.Comment: 20 pages, LaTex 2e, revised version (to appear in Phys. Rev. D

Bosonic Fields in the String-like Defect Model

We study localization of bosonic bulk fields on a string-like defect with codimension 2 in a general space-time dimension in detail. We show that in cases of spin 0 scalar and spin 1 vector fields there are an infinite number of massless Kaluza-Klein (KK) states which are degenerate with respect to the radial quantum number, but only the massless zero mode state among them is coupled to fermion on the string-like defect. It is also commented on interesting extensions of the model at hand to various directions such as 'little' superstring theory, conformal field theory and a supersymmetric construction.Comment: 17 pages, LaTex 2e, revised version (to appear in Phys. Rev. D

Frustration-induced Dodecamer Ordering in the Double-Exchange Spin Ice Model on the Kagom\'e Lattice

We investigate a detail of a dodecamer cluster ordering in a double-exchange spin ice model on a kagom\'e lattice. In frustrated systems, ordinary spin orderings are suppressed and macroscopic degeneracy remains down to low temperatures. In some frustrated systems, the degeneracy is lifted due to residual interactions and cluster orderings are stabilized. In the present model, the spin ice state is first formed at intermediate temperatures, and further entropies are released at lower temperatures as the dodecamer phase emerges. Since the spin symmetry is not broken in the dodecamer phase, there still exists macroscopic degeneracy. At further low temperatures, a possible spin ordering due to inter-dodecamer interactions is proposed. We discuss that such a multiple-site clustering larger than a bond-pair might be generic to frustrated systems where macroscopic degeneracy is lifted by residual interactions.Comment: 18 pages, 11 figure

Extra gauge symmetries in BHT gravity

We study the canonical structure of the Bergshoeff-Hohm-Townsend massive gravity, linearized around a maximally symmetric background. At the critical point in the space of parameters, defined by $\Lambda_0/m^2=-1$, we discover an extra gauge symmetry, which reflects the existence of the partially massless mode. The number of the Lagrangian degrees of freedom is found to be 1. We show that the canonical structure of the theory at the critical point is unstable under linearization.Comment: LATEX, 12 page

Vacuum Structures of Supersymmetric Yang-Mills Theories in 1+11+1 Dimensions

Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$ dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the Born-Oppenheimer approximation for the weak coupling limit, we find that the vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary conditions are also studied, especially the antiperiodic boundary condition for fermions which is related to the system in finite temperatures. In that case we find for gaugino bilinears a nonvanishing vacuum condensation which indicates instanton contributions.Comment: LaTeX file, 25 page, 3 eps figure, some references adde

Direct observation of the flux-line vortex glass phase in a type II superconductor

The order of the vortex state in La_{1.9} Sr_{0.1} CuO_{4} is probed using muon spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally-induced and pinning-induced disorder.Comment: 14 pages, 4 colour figures include

Black-hole dynamics in BHT massive gravity

Using an exact Vaidya-type null-dust solution, we study the area and entropy laws for dynamical black holes defined by a future outer trapping horizon in (2+1)-dimensional Bergshoeff-Hohm-Townsend (BHT) massive gravity. We consider the theory admitting a degenerate (anti-)de Sitter vacuum and pure BHT gravity. It is shown that, while the area of a black hole decreases by the injection of a null dust with positive energy density in several cases, the Wald-Kodama dynamical entropy always increases.Comment: 7 pages, 1 figur

Is every toric variety an M-variety?

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.Comment: 13 page