Testing volume independence of SU(N) pure gauge theories at large N

In this paper we present our results concerning the dependence of Wilson loop expectation values on the size of the lattice and the rank of the SU(N) gauge group. This allows to test the claims about volume independence in the large N limit, and the crucial dependence on boundary conditions. Our highly precise results provide strong support for the validity of the twisted reduction mechanism and the TEK model, provided the fluxes are chosen within the appropriate domain.Comment: 33 pages, latex, 10 figure

Weak Matrix Elements without Quark Masses on the Lattice

We introduce a new parameterization of four-fermion matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties in physical amplitudes. As a result the apparent quadratic dependence of e'/e on m_s is removed. To simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of Renormalization Group Invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of DeltaI=3/2 and SUSY DeltaF=2 (F=S,C,B) four-fermion operators have been computed.Comment: Invited talk at QCD Euroconference 99, 4 pages BUHEP-99-2

N=1 Supersymmetric Yang-Mills on the lattice at strong coupling

We study N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at strong coupling. Our method is based on the hopping parameter expansion in terms of random walks, resummed for any value of the Wilson parameter r in the small hopping parameter region. Results are given for the mesonic (2-gluino) and fermionic (3-gluino) propagators and spectrum.Comment: Latex file. 43 pages. Minor additional comments, references added, typos corrected. Accepted for publication in Int. J. Mod. Phys.

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

Large NN reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure

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