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

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

Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $\epsilon$ $=$ $(4-d)/2$ the coefficients of $\epsilon$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the \overline{\mbox{MS}} scheme at $O(1/N_f)$.Comment: 13 Latex pages, 1 figure (available from author on request), LTH-32

QED corrections to the evolution of parton distributions

We study the systematic inclusion of QED corrections in the evolution of parton distributions. O(alpha) corrections modify the evolution equation for parton distributions. They introduce additional parton distributions, like the photon distribution in the nucleon, and lead to additional mixing effects. We discuss the modifications for a realistic model of N_f,up up-type flavours and N_f,down down-type flavours. We have implemented these corrections into a numerical program and we quantify the size of these effects in a toy model. The corrections reach the order of 1%.Comment: 11 page

Scaling Violations in Yang-Mills Theories and Strings in AdS_5

String solitons in AdS_5 contain information of N=4 SUSY Yang-Mills theories on the boundary. Recent proposals for rotating string solitons reproduce the spectrum for anomalous dimensions of Wilson operators for the boundary theory. There are possible extensions of this duality for lower supersymmetric and even for non-supesymmetric Yang-Mills theories. We explicitly demonstrate that the supersymmetric anomalous dimensions of Wilson operators in N=0,1 Yang-Mills theories behave, for large spin J, at the two-loop level in perturbation theory, like log J. We compile the analytic one- and two-loop results for the N=0 case which is known in the literature, as well as for the N=1 case which seems to be missing.Comment: 16 pages, Appendix included in chapter. Version to appear in Nucl.Phys.

Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes

We generalize the method of our recent paper on the large-spin expansions of Gubser-Klebanov-Polyakov (GKP) strings to the large-spin and large-winding expansions of finite-size giant magnons and finite-size single spikes. By expressing the energies of long open strings in RxS2 in terms of Lambert's W-function, we compute the leading, subleading and next-to-subleading series of classical exponential corrections to the dispersion relations of Hofman-Maldacena giant magnons and infinite-winding single spikes. We also compute the corresponding expansions in the doubled regions of giant magnons and single spikes that are respectively obtained when their angular and linear velocities become smaller or greater than unity.Comment: 43 pages, 13 figures; Matches published version. Rewritten appendix