2,574 research outputs found
Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
We compute the perturbative expression of Wilson loops up to order for
SU() 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 . 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
as a function of flux . 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
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
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 twisted gradient flow running coupling
We measure the running of the 't Hooft coupling by performing a
step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU()
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 , with the torus period. We
set the scale for the running coupling in terms of and use the
gradient flow to define a renormalized 't Hooft coupling .
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
limit taken at fixed value of . The coupling constant is
thus expected to coincide with that of the ordinary pure gauge theory at . 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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