Lower bounds of characteristic scale of topological modification of the Newtonian gravitation

We analytically work out the long-term orbital perturbations induced by the first term of the expansion of the perturbing potential arising from the local modification of the Newton's inverse square law due to a topology R^2 x S^1 with a compactified dimension of radius R recently proposed by Floratos and Leontaris. We neither restrict to any specific spatial direction for the asymmetry axis nor to particular orbital configurations of the test particle. Thus, our results are quite general. Non-vanishing long-term variations occur for all the usual osculating Keplerian orbital elements, apart from the semimajor axis which is left unaffected. By using recent improvements in the determination of the orbital motion of Saturn from Cassini data, we preliminarily inferred R >= 4-6 kau. As a complementary approach, the putative topological effects should be explicitly modeled and solved-for with a modified version of the ephemerides dynamical models with which the same data sets should be reprocessed.Comment: Latex, 6 pages, no tables, 1 figure, 3 references. Accepted for publication in International Journal of Modern Physics D (IJMPD

The Evolution of Unpolarized and Polarized Structure Functions at Small xx

A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic scattering. The available resummed anomalous dimensions are discussed for all these cases, and the most important analytic and numerical results are compiled. The quantitative effects of these small-$x$ resummations on the evolution of the various parton densities and structure functions are presented, and their present uncertainties are investigated. An application to QED radiative corrections is given.Comment: 18 pages Latex, including 11 eps-figures, and a style file. To appear in: Proc. of the International Workshop: QCD and QED in Higher Orders, Rheinsberg, April, 1996, Nucl. Phys. B (Proc. Suppl

Octonionic Gravitational Instantons

We construct eight-dimensional gravitational instantons by solving appropriate self-duality equations for the spin-connection. The particular gravitational instanton we present has $Spin(7)$ holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S^4 and its boundary at infinity is the squashed S^7. We also lift our solutions to ten and eleven dimensions and construct fundamental string and membrane configurations that preserve 1/16 of the original supersymmetries.Comment: 17 pages, latex, no figures. References to earlier works adde

On The Instanton Solutions Of The Self-Dual Membrane In Various Dimensions

We present some methods of determining explicit solutions for self-dual supermembranes in 4+1 and 8+1 dimensions with spherical or toroidal topology. For configurations of axial symmetry, the continuous SU(\infty) Toda equation turns out to play a central role, and a specific method of determining all the periodic solutions are suggested. A number of examples are studied in detail.Comment: Latex, 21p., few typos corrected, version to appear in Phys. Lett.

Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions

We analyze the iterative structure of unfactorized partonic structure functions in the large-x limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions P_gq and P_qg and the corresponding coefficient functions C_phi,q and C_2,g in Higgs- and gauge-boson exchange deep-inelastic scattering. The splitting functions are given in terms of a new function not encountered in perturbative QCD so far, and vanish maximally in the supersymmetric limit C_A - C_F to 0. The coefficient functions do not vanish in this limit, and are given by simple expressions in terms of the above new function and the well-known leading-logarithmic threshold exponential. Our results also apply to the evolution of fragmentation functions and semi-inclusive e^+ e^- annihilation.Comment: 9 pages, LaTeX, 1 eps-figur

Analytic Loops and Gauge Fields

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We show that such representations are closely associated with the (anti-)self-dual Yang-Mills equations in ${\bf R}^8$Comment: 10 pages, LaTeX, no figure

Solutions of the Generic Non-Compact Weyl Equation

In this paper, solutions of the generic non-compact Weyl equation are obtained. In particular, by identifying a suitable similarity transformation and introducing a non-trivial change of variables we are able to implement azimuthal dependence on the solutions of the diagonal non-compact Weyl equation. We also discuss some open questions related to the construction of infinite BPS monopole configurations.Comment: 12 pages, Latex. Few extra comments and a reference adde

Evolution Kernels from Splitting Amplitudes

We recalculate the next-to-leading order Altarelli-Parisi kernel using a method which relates it to the splitting amplitudes describing the collinear factorization properties of scattering amplitudes. The method breaks up the calculation of the kernel into individual pieces which have an independent physical interpretation.Comment: References adde

Eight-Dimensional Self-Dual Spaces

We discuss higher-dimensional gravitational instantons by studying appropriate self-duality equations for the spin connection. In seven and in eight dimensions, the corresponding spaces admit a covariantly constant spinor and have holonomies in G_2 and Spin(7), respectively. We find a non-compact solution to the self-duality equations in eight dimensions in which the self-dual space has an elliptically-fibered structure.Comment: 16 pages, late