Discrete symmetries in higher dimensions

We consider the constraints imposed by causality on the transformations of time reversal ?, charge conjugationC, and parityP in higher dimensional space-time.     

Grand unification in higher dimensions

We have recently proposed an alternative picture for the physics at the scale of gauge coupling unification, where the unified symmetry is realized in higher dimensions but is broken locally by a symmetry breaking defect. Gauge coupling unification, the quantum numbers of quarks and leptons and the longevity of the proton arise as phenomena of the symmetrical bulk, while the lightness of the Higgs doublets and the masses of the light quarks and leptons probe the symmetry breaking defect. Moreover, the framework is extremely predictive if the effective higher dimensional theory is valid over a large energy interval up to the scale of strong coupling. Precise agreement with experiments is obtained in the simplest theory—SU(5) in five dimensions with two Higgs multiplets propagating in the bulk. The weak mixing angle is predicted to be sin²θ_w=0.2313±0.0004, which fits the data with extraordinary accuracy. The compactification scale and the strong coupling scale are determined to be and , respectively. Proton decay with a lifetime of order is expected with a variety of final states such as e⁺π⁰, and several aspects of flavor, including large neutrino mixing angles, are understood by the geometrical locations of the matter fields. When combined with a particular supersymmetry breaking mechanism, the theory predicts large lepton flavor violating μ→e and τ→μ transitions, with all superpartner masses determined by only two free parameters. The predicted value of the bottom quark mass from Yukawa unification agrees well with the data. This paper is mainly a review of the work presented in hep-ph/0103125, hep-ph/0111068, and hep-ph/0205067 [1], [2] and [3].     

Integrable classical systems in higher dimensions

A general method for the construction of the second constant of motion (up to second order) for higher-dimensional classical systems is carried out. Correspondingly, the first- and the second-order potential equations are obtained whose solutions can directly provide the integrable systems.     

The Vaidya solution in higher dimensions

The Vaidya metric representing the gravitational field of a radiating star is generalized to spacetimes of dimensions greater than four.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Calogero-Sutherland type models in higher dimensions

We construct two different Calogero-Sutherland type models with only two-body interactions in arbitrary dimensions. We obtain some exact wave functions, including the ground states, of these two models for an arbitrary number of spinless nonrelativistic particles.     

The superconformal algebra in higher dimensions

The superconformal algebra for 4/4N-dimensional super-Minkowski space (d=4) can be identified with the simple superalgebra su (2,2/N). For even-dimension d=5,6 the superconformal algebra can be identified with a real form of the simple superalgebras F(4), D(4,1) respectively in Kac's classification. For even-dimension d>-7 it is impossible to define a superconformal algebra satisfying three natural conditions: (1) it acts as infinitesimal automorphisms on super-Minkowski space; (2) this action extends the natural action of the super-Poincaré algebra; (3) when the action of the even part of the superconformal algebra is reduced to an infinitesimal action on ordinary Minkowski space, it extends the natural action of the conformal algebra so (2, d).     

Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.     

Non perturbative anomalies in higher dimensions

We study how nonperturbative anomalies can occur in dimensions higher than four and their implications on the consistency of the theory.     

Explicit and implicit FEM-FCT algorithms with flux linearization

A new approach to the design of flux-corrected transport (FCT) algorithms for continuous (linear/multilinear) finite element approximations of convection-dominated transport problems is pursued. The algebraic flux correction paradigm is revisited, and a family of nonlinear high-resolution schemes based on Zalesak’s fully multidimensional flux limiter is considered. In order to reduce the cost of flux correction, the raw antidiffusive fluxes are linearized about an auxiliary solution computed by a high- or low-order scheme. By virtue of this linearization, the costly computation of solution-dependent correction factors is to be performed just once per time step, and there is no need for iterative defect correction if the governing equation is linear. A predictor–corrector algorithm is proposed as an alternative to the hybridization of high- and low-order fluxes. Three FEM-FCT schemes based on the Runge–Kutta, Crank–Nicolson, and backward Euler time-stepping are introduced. A detailed comparative study is performed for linear convection–diffusion equations.     

Global symmetries in four and higher dimensions

Knowing that a four-dimensional theory with gauge group G₀ is unified in theory with gauge group G puts restrictions on what global symmetries are possible in the low-energy world. Here we analyze those restrictions assuming that unification in G occurs inn four dimensions and assuming that unification occurs only in a higher-dimensional theory. There are possibilities for global symmetries which are not possible in the former case, so in principle indirect evidence for higher dimensions might be found by finding peculiar global symmetries in the low-energy world.     

Charged BTZ-like black holes in higher dimensions

Motivated by many worthwhile papers about (2+1)-dimensional BTZ black hole solutions, we generalize them to (n+1)-dimensional solutions, the so-called BTZ-like solutions. We show that the electric field of BTZ-like solutions is the same as that of (2+1)-dimensional BTZ black holes, and also their lapse functions are approximately the same, too. By these similarities, it is also interesting to investigate the geometric and thermodynamics properties of the BTZ-like solutions. We find that, depending on the metric parameters, the BTZ-like solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons, an extreme black hole or naked singularity. Then, we obtain the conserved and thermodynamic quantities, and we show that they satisfy the first law of thermodynamics. Next, we perform a thermodynamic stability analysis in the canonical ensemble and find that the BTZ-like solutions are stable in the whole phase space.     

The generalized Maxwell-Einstein system in higher dimensions

We study some consequences of the generalized Maxwell-Einstein system in higher dimensions. This generalization is such that the Maxwell-type field constructed in an evenn-dimensional space-time preserves the conformal invariance. After dimensional reduction to four dimensions, it gives rise to scalar, electromagnetic and Kalb-Ramond fields. Specifically, we analyse here some compactification processes, including the stability of the final configuration (forn=8), and anisotropic cosmological solutions (forn=6).On leave of absence from: Departamento de Física e Química, Universidade Federal do Espírito Santo, Goiabeiras, Vitória CEP 29000, Espírito Santo, Brazil     

Existence of solitary waves in higher dimensions

The elliptic equation u=F(u) possesses non-trivial solutions inR ⁿ which are exponentially small at infinity, for a large class of functionsF. Each of them provides a solitary wave of the nonlinear Klein-Gordon equation.This work was supported in part by NSF Grant MCS 75-08827     

Wormholes in higher dimensions with Gauss-Bonnet terms

A class of wormhole solutions permitted in a theory with Gauss-Bonnet terms in the gravitational action in higher dimensions have been studied. The case of de-Sitter type instantons, with a compact inner space, are of particular interest here. Some of the configurations, when continued analytically to the Lorentzian metric lead to the standard inflationary universe. Some multiple-sphere configurations of the type studied by Myers have also been noted. The Euclidean action for the solutions has been calculated and the relevance of the solutions in the quantum creation of the universe has been considered.     

Spherical symmetry and mass-energy in higher dimensions

The components of the Einstein tensor and other relations are given for a spherically symmetric metric in null coordinates in higher dimensions. These relations are particularly relevant to the study of gravitational collapse of a perfect fluid with heat flow but without viscosity, where the exterior space cannot be considered as vacuum and matching to Schwarzschild space-time is not suitable. The analysis generalizes to higher dimensions work of Cahill and McVittie in 4D space-time. Using the expression for the mass function, it is observed that pressure vanishes at the boundary of the distribution for a perfect fluid in the higher-dimensional case also, but the same is not true when heat flow is considered.