39 research outputs found
Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions
It is well known that in four or more dimensions, there exist exotic
manifolds; manifolds that are homeomorphic but not diffeomorphic to each other.
More precisely, exotic manifolds are the same topological manifold but have
inequivalent differentiable structures. This situation is in contrast to the
uniqueness of the differentiable structure on topological manifolds in one, two
and three dimensions. As exotic manifolds are not diffeomorphic, one can argue
that quantum amplitudes for gravity formulated as functional integrals should
include a sum over not only physically distinct geometries and topologies but
also inequivalent differentiable structures. But can the inclusion of exotic
manifolds in such sums make a significant contribution to these quantum
amplitudes? This paper will demonstrate that it will. Simply connected exotic
Einstein manifolds with positive curvature exist in seven dimensions. Their
metrics are found numerically; they are shown to have volumes of the same order
of magnitude. Their contribution to the semiclassical evaluation of the
partition function for Euclidean quantum gravity in seven dimensions is
evaluated and found to be nontrivial. Consequently, inequivalent differentiable
structures should be included in the formulation of sums over histories for
quantum gravity.Comment: AmsTex, 23 pages 5 eps figures; replaced figures with ones which are
hopefully viewable in pdf forma
The index of symmetry of compact naturally reductive spaces
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold.submittedVersionFil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Tamuru, Hiroshi. Universidad de Hiroshima. Escuela de Ciencias. Departamento de Matemática; Japón.Matemática Pur
M-Theory on Spin(7) Manifolds
We study M-theory on two classes of manifolds of Spin(7) holonomy that are
developing an isolated conical singularity. We construct explicitly a new class
of Spin(7) manifolds and analyse in detail the topology of the corresponding
classical spacetimes. We discover also an intricate interplay between various
anomalies in M-theory, string theory, and gauge theory within these models, and
in particular find a connection between half-integral G-fluxes in M-theory and
Chern-Simons terms of the N=1, D=3 effective theory.Comment: 81 pages; minor corrections/clarifications, references adde
Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
In this paper, we look for metrics of cohomogeneity one in D=8 and D=7
dimensions with Spin(7) and G_2 holonomy respectively. In D=8, we first
consider the case of principal orbits that are S^7, viewed as an S^3 bundle
over S^4 with triaxial squashing of the S^3 fibres. This gives a more general
system of first-order equations for Spin(7) holonomy than has been solved
previously. Using numerical methods, we establish the existence of new
non-singular asymptotically locally conical (ALC) Spin(7) metrics on line
bundles over \CP^3, with a non-trivial parameter that characterises the
homogeneous squashing of CP^3. We then consider the case where the principal
orbits are the Aloff-Wallach spaces N(k,\ell)=SU(3)/U(1), where the integers k
and \ell characterise the embedding of U(1). We find new ALC and AC metrics of
Spin(7) holonomy, as solutions of the first-order equations that we obtained
previously in hep-th/0102185. These include certain explicit ALC metrics for
all N(k,\ell), and numerical and perturbative results for ALC families with AC
limits. We then study D=7 metrics of holonomy, and find new explicit
examples, which, however, are singular, where the principal orbits are the flag
manifold SU(3)/(U(1)\times U(1)). We also obtain numerical results for new
non-singular metrics with principal orbits that are S^3\times S^3. Additional
topics include a detailed and explicit discussion of the Einstein metrics on
N(k,\ell), and an explicit parameterisation of SU(3).Comment: Latex, 60 pages, references added, formulae corrected and additional
discussion on the asymptotic flow of N(k,l) cases adde
Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
We study aspects of superstring vacua of non-compact special holonomy
manifolds with conical singularities constructed systematically using soluble N
= 1 superconformal field theories (SCFT's). It is known that Einstein
homogeneous spaces G/H generate Ricci flat manifolds with special holonomies on
their cones R_+ x G/H, when they are endowed with appropriate geometrical
structures, namely, the Sasaki-Einstein, tri-Sasakian, nearly Kahler, and weak
G_2 structures for SU(n), Sp(n), G_2, and Spin(7) holonomies, respectively.
Motivated by this fact, we consider the string vacua of the type: R^{d-1,1} x
(N = 1 Liouville) x (N=1 supercoset CFT on G/H) where we use the affine Lie
algebras of G and H in order to capture the geometry associated to an Einstein
homogeneous space G/H. Remarkably, we find the same number of spacetime and
worldsheet SUSY's in our ``CFT cone'' construction as expected from the
analysis of geometrical cones over G/H in many examples. We also present an
analysis on the possible Liouville potential terms (cosmological constant type
operators) which provide the marginal deformations resolving the conical
singularities.Comment: 60 pages, no figure, 2 tables; v2 typos correcte
استخدام الانظمة المتسقة في تقسيم الترددات المتعامدة في انظمة الاتصالات الضوئية
Orthogonal frequency division multiplexing (OFDM) has quickly gained its attraction in optical communications that are evolving towards software-enhanced optical transmissions. Coherent optical OFDM (CO-OFDM) takes advantage of software capabilities of electronic digital signal processing (DSP) to perform sophisticated operations and has demonstrated its easiness of realizing high spectral efficiency and combating various distortions at the same time. Coherent optical OFDM (CO-OFDM) has attracted lots of interest due to its high spectral efficiency (SE) and robustness to fiber dispersion and is considered as a promising candidate for long haul optical fiber transmission systems. In the beginning of this study, we will focus in (OFDM) theoretically with basic initial concepts, then a theoretical study of (CO-OFDM) and Direct detection (DD-OFDM) systems in deep with comparing between them, and identifying the advantages and disadvantages for both systems. Next, a practical study for the previous systems, by using (Optisystem), a special simulation program to simulate and analyze the system. This simulation we will simulate (CO-OFDM) for long-haul transmissions with its analysis such as optical signal to noise ratio (OSNR), RF spectrum, and constellation diagrams .In addition, we will simulate (DD-OFDM) with the same previous parameters and compare between the two systems .Then, we will compare (CO-OFDM) with dispersion compensating fiber (DCF) as a treatment to increase the transmission distance. Finally, we will integrate the wavelength division multiplexing system (WDM) with (CO-OFDM) system, to increase the system performance and achieve high data rates