2,574 research outputs found

    Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

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    We compute the perturbative expression of Wilson loops up to order g4g^4 for SU(NN) lattice gauge theories with Wilson action on a finite box with twisted boundary conditions. Our formulas are valid for any dimension and any irreducible twist. They contain as a special case that of the 4-dimensional Twisted Eguchi-Kawai model for a symmetric twist with flux kk. Our results allow us to analyze the finite volume corrections as a function of the flux. In particular, one can quantify the approach to volume independence at large NN as a function of flux kk. The contribution of fermion fields in the adjoint representation is also analyzed.Comment: pdflatex 57 pages, 9 figures, 4 appendice

    Volume dependence in 2+1 Yang-Mills theory

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    We present the results of an analysis of a 2+1 dimensional pure SU(N) Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial magnetic flux. We focus on investigating the dependence of the electric-flux spectrum, extracted from Polyakov loop correlators, with the spatial size l, the number of colours N, and the magnetic flux m. The size of the torus acts a parameter that allows to control the onset of non-perturbative effects. In the small volume regime, where perturbation theory holds, we derive the one-loop self-energy correction to the single-gluon spectrum, for arbitrary N and m. We discuss the transition from small to large volumes that has been investigated by means of Monte-Carlo simulations. We argue that the energy of electric flux e, for the lowest gluon momentum, depends solely on e/N and on the dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The variable x can be interpreted as the dimensionless 't Hooft coupling for an effective box size given by Nl. This implies a version of reduction that allows to trade l by N without modifying the electric-flux energy.Comment: 7 pages, 3 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia. Minor change: Fig. 1 modified to correctly account for the sign convention in Eq. (2.5

    Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics

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    We present a detailed study of a filtering method based upon Dirac quasi-zero-modes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte Carlo dynamics on topological structures like instantons.Comment: 39 pages, 15 figure

    The SU(∞)SU(\infty) twisted gradient flow running coupling

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    We measure the running of the SU(∞)SU(\infty) 't Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU(NN) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameter l~=lN\tilde l = l \sqrt{N}, with ll the torus period. We set the scale for the running coupling in terms of l~\tilde l and use the gradient flow to define a renormalized 't Hooft coupling λ(l~)\lambda(\tilde l). In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large NN limit taken at fixed value of λ(l~)\lambda(\tilde l). The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at N=∞N =\infty. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling.Comment: 22 pages, 7 figure
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