A Note on the Supersymmetries of the Self-Dual Supermembrane

In this letter we discuss the supersymmetry issue of the self dual supermembranes in (8+1) and (4+1)-dimensions. We find that all genuine solutions of the (8+1)-dimensional supermembrane, based on the exceptional group G_2, preserve one of the sixteen supersymmetries while all solutions in (4+1)-dimensions preserve eight of them.Comment: Latex file, 12pages, no figure

Non-commutative Solitons in Finite Quantum Mechanics

We construct the unitary evolution operators that realize the quantization of linear maps of SL(2,R) over phase spaces of arbitrary integer discretization N and show the non-trivial dependence on the arithmetic nature of N. We discuss the corresponding uncertainty principle and construct the corresponding coherent states, that may be interpreted as non-commutative solitons.Comment: 3 pages LaTeX. Uses espcrc2.sty and amssymb.sty. Contribution to Lattice 2002(theoretical

Non-Collapsing Membrane Instantons in Higher Dimensions

We introduce a particular embedding of seven dimensional self-duality membrane equations in C^3\times R which breaks G_2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C^3. We discuss in detail solutions for spherical and toroidal topologies assuming factorization of time. We show that the extra dimensions manifest themselves in the solutions through the appearance of a non-zero conserved charge which prevents the collapse of the membrane. We find non-collapsing rotating membrane instantons which contract from infinite size to a finite one and then they bounce to infinity in finite time. Their motion is periodic. These generalized complex Nahm equations, in the axially symmetric case, lead to extensions of the continuous Toda equation to complex space.Comment: 14 pages, 2 figure

Gauge theories and non-commutative geometry

It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry. In this paper we present an explicit proof for the case of the torus and the sphere.Comment: 12 page

Low Scale Unification, Newton's Law and Extra Dimensions

Motivated by recent work on low energy unification, in this short note we derive corrections on Newton's inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the corrections are of Yukawa type. Inside the compactified space of n-extra dimensions the sub-leading term is proportional to the (n+1)- power of the distance over the compactification radius ratio. Some physical implications of these modifications are briefly discussed.Comment: 12pages, 2 figure

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

Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/N_f)

Using large N_f methods we compute the anomalous dimension of the predominantly gluonic flavour singlet twist-2 composite operator which arises in the operator product expansion used in deep inelastic scattering. We obtain a d-dimensional expression for it which depends on the operator moment n. Its expansion in powers of epsilon = (4-d)/2 agrees with the explicit exact three loop MSbar results available for n less than or equal to 8 and allows us to determine some new information on the explicit n-dependence of the three and higher order coefficients. In particular the n-dependence of the three loop anomalous dimension gamma_{gg}(a) is determined in the C_2(G) sector at O(1/N_f).Comment: 26 latex pages, 7 postscript figure

Octonionic Selfduality for SuperMembranes

In this work we study the recently introduced octonionic duality for membranes. Restricting the self - duality equations to seven space dimensions, we provide various forms for them which exhibit the symmetries of the octonionic and quaternionic structure. These forms may turn to be useful for the question of the integrability of this system. Introducing a consistent quadratic Poisson algebra of functions on the membrane we are able to factorize the time dependence of the self - duality equations. We further give the general linear embeddings of the three dimensional system into the seven dimensional one using the invariance of the self-duality equations under the exceptional group G_2.Comment: Latex file, 21 page

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

Joint resummation in electroweak boson production

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.Comment: 27 pages, LaTeX, 8 figures as eps files. Some additions to earlier version, this version as published in Phys. Rev. D66 (2002) 01401