New Taub–NUT–Reissner–Nordström spaces in higher dimensions

We construct new charged solutions of the Einstein–Maxwell field equations with cosmological constant. These solutions describe the nut-charged generalisation of the higher-dimensional Reissner–Nordström spacetimes. For a negative cosmological constant these solutions are the charged generalizations of the topological nut-charged black hole solutions in higher dimensions. Finally, we discuss the global structure of such solutions and possible applications.     

Massive particles in five dimensions

We consider a five-dimensional model of the universe with a dynamical extra dimension. Calculations of the ratio of the number density of Kolb and Slansky type pyrgons to that photons show the model to be uncacceptable. However by inserting N matter fields into the original action, it becomes possible to reduce the ratio below the observational bound.     

The supercurrent in five dimensions

The supercurrent multiplet is constructed for N=2 and 4 extended supersymmetries in five dimensions. The corresponding supergravity multiplets are also exhibited and have 40 + 40 and 128 + 128 components, respectively.     

Ising droplets in five dimensions

Monte Carlo simulations indicate that the size distribution of Coniglio-Klien droplets in the five-dimensional nearest-neighbor Ising model corresponds to mean field Ising exponents.     

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].     

Ricci-flat and charged wormholes in five dimensions

We construct stationary Ricci-flat inter-universe Lorentzian wormhole solutions in all D?5$D?5$ dimensions that connect two flat asymptotic spacetimes. Such a solution can be viewed as the gravity dual of a string tachyon state whose linear momentum is larger than its tension. We focus our analysis on the D=5$D=5$ wormholes which are not traversable for the timelike and null geodesics; however, we demonstrate that there exist accelerated timelike trajectories that traverse from one asymptotic region to the other. We further study the minimally-coupled scalar wave equation and demonstrate that the quantum tunnelling between two worlds must occur. We also obtain charged wormholes in five-dimensional supergravities. With appropriate choice of parameters, these wormholes connect AdS₃×S²${\mathit{AdS}}_3\times S^2$ in one asymptotic region to flat Minkowskian spacetime in the other.     

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.     

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.     

Exceptional coset spaces and unification in six dimensions

The coset spaces E₈/SO(10)×H_F allow complex structures which can account for three quark–lepton generations including right-handed neutrinos. We show that in the context of supersymmetric SO(10) gauge theories in 6 dimensions they also provide the Higgs fields which are needed to break the electroweak and B−L gauge symmetries, and to generate small neutrino masses via the seesaw mechanism.     

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.     

General relativity and quantum mechanics in five dimensions

In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how general relativity and quantum mechanics may be unified in 5D.     

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.     

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.     

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.