Odd Number Of Dimensions Research Articles

Odd dimensional nonlocal Liouville conformal field theories

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a mathcal{Q} -curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function F, the boundary conformal anomaly and vertex operators’ correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.

Corrections to the Hawking Tunneling Radiation from MDR

We investigate some aspects of black hole (BH) thermodynamics in the framework of a modified dispersion relation. We calculate a minimal length and a maximal momentum to find a relation between spacetime dimensions and the presence of logarithmic prefactor in the black hole entropy relation. We show that the logarithmic prefactor appears not only in an even number of dimensions but also in an odd number of dimensions. In addition, the sign of the logarithmic factor is different for positive values of α in all dimensions. Using the corrected entropy, the black hole radiation probability is calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and shows a more probable quantum tunneling.

An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically at vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.

Higher dimensional rotating black holes in Einstein–Maxwell theory with negative cosmological constant

We present arguments for the existence of charged, rotating black holes with equal-magnitude angular momenta in an odd number of dimensions D⩾5. These solutions possess a regular horizon of spherical topology and approach asymptotically the anti-de Sitter spacetime background. We analyze their global charges, their gyromagnetic ratio and their horizon properties.

Gravitational perturbations of higher dimensional rotating black holes: Tensor perturbations

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the endpoint of the instability may be a stationary, nonaxisymmetric black hole.

Spherically Symmetric Logistic Distribution

In this paper exact formulae of the probability density function for the spherically symmetric distribution with marginal logistic are given. They are entirely different for odd and even dimensions. For an odd number of dimensions it is possible to express them by elementary functions but for an even number of dimensions, it is possible only by an infinite series of functions. These series, however, are very convenient for computations and could be useful in practice.

Huyghens’ principle in (2n+1) dimensions for nonlocal pseudodifferential operators of the type □α

The validity of the Huyghens principle for half-integer powers of the D’Alembertian in odd number of dimensions is discussed. It is shown in particular that for □1/2 in 2+1 the dynamic of □ in 3+1 is obtained.

PARITY-VIOLATING ANOMALY FROM THE FOKKER-PLANCK EQUATION

We compute parity-violating anomaly in gauge theories with odd number of dimensions using an approach based on the effective Fokker-Planck equation in the stochastic quantization scheme. We find results that agree with those obtained by the Langevin equation.

Topological mass quantization and parity violation in 2 + 1 dimensional QED

We give a quantization condition for the coefficient of the topological mass term and a topological argument for the necessity of parity violation in a 2 + 1 dimensional QED, and in general in an odd number of dimensions. We also point out and rectify a technical flaw in the standard argument for the SU(2) nonperturbative anomaly.

Spectral flow and the anomalous production of fermions in odd number of dimensions.

The relationship between instantons and the index-theory analysis of anomalies is examined in odd-dimensional gauge theories. Consistency of the anomalous production of fermions associated with nontrivial spectral flows of Dirac Hamiltonians and the absence of odd-dimensional anomalies in continuous symmetries is clarified. A new structure of three-dimensional matter is suggested.

A Transversely Isotropic Elliptic Equation: An ARR Analogy Approach

A “specially” elliptic equation is posed for a singular point source within a transversely isotropic medium. This occupies an infinite space with an odd number of dimensions equaling or exceeding three. By appropriately transforming the given equation, one can deduce an implicit solution anywhere off a source plane. This is done through an analogy with the time-dependent ARR problem [4] involving an even number of spatial dimensions. Explicit results can be established, as well as eigenfunction behavior near the symmetry axis. Principles are illustrated with an application to an elastodynamic problem for a propagating concentrated force.

On the classical approximation involved in the Thomas-Fermi theory

The nature of the expansion of the particle density of a system in powers of h is investigated. An exact expression for the density in a system with an harmonic potential is obtained. There are two types of terms. First, there are steady terms which agree with those derived by other authors and yield in first approximation the Thomas-Fermi result. Secondly, there are oscillatory terms analogous to the de Haas-van Alphen terms in the susceptibility of an electron gas and which cannot be expanded in powers of h . For systems with an odd number of dimensions the series of steady terms is shown to be divergent for all values of h =(= 0. If the number of dimensions is even there is only a finite number of steady terms.

On a regular Cauchy problem for the Euler—Poisson—Darboux equation

A new method is given for solving the wave equation in space of any odd number of dimensions without making use of any device for evaluating divergent integrals. This gives the clue to a simple method of solving the regular Cauchy problem for the so-called Euler-Poisson-Darboux equation in space of any odd number of dimensions, a problem which has previously only been solved by a very difficult extension of Marcel Riesz’s method.