Improvement of the Rotation Arch of the Posterior Interosseous Pedicle Flap Preserving Both Reverse Posterior and Anterior Interosseous Vascular Sources.

Abstract PURPOSE: The reverse posterior interosseous artery flap has several advantages, not sacrificing any major blood vessel, but its relatively short pedicle limits the use to cover defects up to the metacarpophalangeal joint. Our purpose is to demonstrate that the ligature of the anterior interosseous artery (AIA), proximal to the communicating branch with the posterior interosseous artery, leads to an improved flap rotation arch, preserving both vascular sources. METHODS: Sixteen fresh cadavers with latex perfusion were analyzed before and after our technique of elongation, and the so-obtained measures were standardized in "percentage of elongation of the pedicle." Eight patient with the loss of substance at the dorsal aspect of the hand have been treated with this technique, and results were evaluated in terms of flap survival and complication rates. RESULTS: The medium length of the pedicle in the normal flap was 10.8\u2009cm, and after the section of the AIA, the medium length of the pedicle was 13.6\u2009cm with a medium increase of 2.8\u2009cm. It means a medium increase of 24% of the length of the pedicle. In all patients treated, full coverage of the defect was obtained, and we did not experience major complications. CONCLUSIONS: This anatomical study supported by our clinical experience demonstrates that the use of the variant described above permits to reach more distal part of the hand without being afraid to stretch the pedicle because of the connection with the anastomotic arcades of the AIA at the wrist reducing the risk of ischemia of the flap

Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription

We find the exact non-perturbative expression for a simple Wilson loop of arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription. The result differs from the standard pure exponential area-law of YM_2, but still exhibits confinement as well as invariance under area-preserving diffeomorphisms and generalized axial gauge transformations. We show that the large N limit is NOT a good approximation to the model at finite N and conclude that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound state solutions. The main significance of our results derives from the importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE

Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions

A light-like Wilson loop is computed in perturbation theory up to ${\cal O} (g^4)$ for pure Yang--Mills theory in 1+1 dimensions, using Feynman and light--cone gauges to check its gauge invariance. After dimensional regularization in intermediate steps, a finite gauge invariant result is obtained, which however does not exhibit abelian exponentiation. Our result is at variance with the common belief that pure Yang--Mills theory is free in 1+1 dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

We study correlation functions of Wilson loops and local operators in a subsector of N=4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In turn, this can be reduced to computing correlators in certain Gaussian multi-matrix models. We focus on the correlation function of a Wilson loop and two local operators, and solve the corresponding three-matrix model exactly in the planar limit. We compare the strong coupling behavior to string theory in AdS_5xS^5, finding precise agreement. We pay particular attention to the case in which the local operators have large R-charge J \sim sqrt{lambda} at strong coupling.Comment: 50 pages, 9 figures. v2: minor changes, references adde

The light-cone gauge and the calculation of the two-loop splitting functions

We present calculations of next-to-leading order QCD splitting functions, employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP). In contrast to the `principal-value' prescription used in the original CFP paper for dealing with the poles of the light-cone gauge gluon propagator, we adopt the Mandelstam-Leibbrandt prescription which is known to have a solid field-theoretical foundation. We find that indeed the calculation using this prescription is conceptionally clear and avoids the somewhat dubious manipulations of the spurious poles required when the principal-value method is applied. We reproduce the well-known results for the flavour non-singlet splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting function, which are the most complicated ones, and which provide an exhaustive test of the ML prescription. We also discuss in some detail the x=1 endpoint contributions to the splitting functions.Comment: 41 Pages, LaTeX, 8 figures and tables as eps file

Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this treatment to the case of U(N) Yang-Mills defined on the noncommutative plane. We deal with all the subtleties which arise in their two-dimensional geometric procedure, using where needed results from the perturbative computations of the noncommutative Wilson loop available in the literature. The open Wilson line contribution present in the non-commutative version of the loop equation drops out in the resulting usual differential equations. These equations for all N have the same form as in the commutative case for N to infinity. However, the additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.Comment: 20 pages, 3 figures, references added, small clarifications adde

Extraction of the x-dependence of the non-perturbative QCD b-quark fragmentation distribution component

Using recent measurements of the b-quark fragmentation distribution obtained in $e^+e^- \to b \bar{b}$ events registered at the Z pole, the non-perturbative QCD component of the distribution has been extracted independently of any hadronic physics modelling. This distribution depends only on the way the perturbative QCD component has been defined. When the perturbative QCD component is taken from a parton shower Monte-Carlo, the non-perturbative QCD component is rather similar with those obtained from the Lund or Bowler models. When the perturbative QCD component is the result of an analytic NLL computation, the non-perturbative QCD component has to be extended in a non-physical region and thus cannot be described by any hadronic modelling. In the two examples used to characterize these two situations, which are studied at present, it happens that the extracted non-perturbative QCD distribution has the same shape, being simply translated to higher-x values in the second approach, illustrating the ability of the analytic perturbative QCD approach to account for softer gluon radiation than with a parton shower generator.Comment: 13 page

Cross section of the processes e++e−→e++e−(γ)e^++e^-\to e^++e^-(\gamma), →π++π−(γ)\to \pi^++\pi^-(\gamma), μ++μ−(γ) \mu^++\mu^-(\gamma), γ+γ(γ) \gamma+\gamma(\gamma) in the energy region 200 MeV ≤2E≤\le 2E\le 3 GeV

The cross section for different processes induced by $e^+e^-$ annihilation, in the kinematical limit $\beta_{\mu}\approx\beta_{\pi}=(1-m_{\pi}^2/\epsilon^2)^{1/2}\sim 1$, is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy $\omega\le\Delta E\le \epsilon$ in the center of mass of the $e^+e^-$ colliding beams. The results are given separately for charge--odd and charge--even terms in the final channels $\pi^+\pi^-(\gamma)$ and $\mu^+\mu^-(\gamma)$. In case of pions, form factors are taken into account. The differential cross sections for the processes: $e^++e^-\to e^++e^-(+\gamma)$, $\to \pi^++\pi^-(\gamma)$, $\to \mu^++\mu^-(\gamma),\to \gamma\gamma(\gamma)$ have been calculated and the corresponding formula are given in the ultrarelativistic limit $\sqrt{s}/2= \epsilon \gg m_{\mu}\sim m_{\pi}$ . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of $\pi^+\pi^-$, including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.Comment: 25 pages 3 firgur

Morita Duality and Noncommutative Wilson Loops in Two Dimensions

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.Comment: 32 pages, 9 figures; v2: clarifying comments added; Final version to be published in JHE

On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.Comment: LaTeX JHEP style, 16 pages, 2 figure