The string tension for Large N gauge theory from smeared Wilson loops

Using smeared Creutz ratios we extract the string tension for SU(N) pure gauge theory and $N$=3,4,5,6,8. We employ these results to extrapolate to large N. The same methodology is applied to the single-site Twisted Eguchi Kawai model. The corresponding string tension matches perfectly within errors with the extrapolated one, providing strong evidence in favour of the twisted reduction framework. Interesting results are also obtained on the behaviour of Creutz ratios for large sizes.Comment: 7 pages and 3 figures. Contribution to Lattice 2012 in Cairn

The string tension from smeared Wilson loops at large N

We present the results of a high statistics analysis of smeared Wilson loops in 4 dimensional SU(N) Yang-Mills theory for various values of N. The data is used to analyze the behaviour of smeared Creutz ratios, extracting from them the value of the string tension and other asymptotic parameters. A scaling analysis allows us to extrapolate to the continuum limit for N=3,5,6 and 8. The results are consistent with a $1/N^2$ approach towards the large N limit. The same analysis is done for the TEK model (one-point lattice) for N=841 and a non-minimal symmetric twist with flux of $k=9$. The results match perfectly with the extrapolated large N values, confirming the validity of the reduction idea for this range of parameters.Comment: Enlarged revised version with 2 tables and 3 figure

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

Twisted reduction in large N QCD with adjoint Wilson fermions

The twisted space-time reduced model of large $N$ QCD with various flavours of adjoint Wilson fermions is constructed applying the symmetric twist boundary conditions with flux $k$. The models with one and two flavours show distinctive behaviours. For the two flavor case, the string tension, calculated at $N=289$, approaches zero as we decrease the quark mass in a way consistent with the theory being governed by an infrared fixed point. In contrast, the string tension for the case of a single adjoint Wilson fermion remains finite as the quark mass decreases to zero, supporting that this is a confining theory.Comment: 7 pages, 8 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Large N meson masses from a matrix model

We explain how to compute meson masses in the large $N$ limit using the twisted Eguchi-Kawai model. A very simple formula is derived, and we show how it leads in a fast and efficient way to results which are in fairly good agreement with other determinations. The method is easily extensible to reduced models with dynamical fermions based on the twisted reduction idea.Comment: latex 14 pages and 3 figure

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

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

We compute the perturbative expression of Wilson loops up to order $g^4$ for SU($N$) 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 $k$. 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 $N$ as a function of flux $k$. The contribution of fermion fields in the adjoint representation is also analyzed.Comment: pdflatex 57 pages, 9 figures, 4 appendice