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

Blog as a teaching and learning of languages

Resumen tomado de la publicaciónTítulo, resumen y palabras clave también en inglésLas actuales corrientes pedagógicas proponen un enfoque constructivista (teorías de Vigotsky [Ivic, 1994]) y un aprendizaje colaborativo (Ausubel y Novak [Daley, 2010]); por lo que las analogías con la Web 2.0 son evidentes, pues ésta se basa en la creación de conocimiento compartido. El término Web 2.0 está asociado con aplicaciones web para compartir información y una de las herramientas utilizadas es el blog. Se pretende familiarizar al profesorado y al alumnado implicado con esta herramienta. Respecto al aprendizaje de la lengua en sí misma, se persigue una mejora de las cuatro destrezas comunicativas. Se utiliza la herramienta en el aula, pero se fomenta el aprendizaje autónomo, método especialmente útil en este tipo de centros. No se utiliza el blog como una simple bitácora, sino que se transforma en un medio para crear una interacción entre el alumnado, promoviendo así el aprendizaje colaborativo. Se propone el uso de los blogs como un elemento adicional a las clases, bien como un refuerzo o como profundización y ampliación de conocimientos lingüísticos y culturales, pero nunca como un sustituto de éstas.ES

The sphaleron energy for SU(2)-Higgs from cooling

The cooling algorithm for saddle points presented in ref. [1] is generalized to obtain static classical solutions of the SU(2)-Higgs field theory in the limit of infinite Higgs self-coupling. The sphaleron energy obtained via this algorithm is ${\cal E}_{\rm sph}= 5.08(7)\,M_W/\alpha_W$ to be compared with 5.0707 obtained in the variational approach [2].Comment: 3 pages, uuencoded compressed PostScript file. Contribution to Lattice '94, 27 Sep - 1 Oct 1994, Bielefeld, German

Topology by improved cooling: susceptibility and size distributions

We use a cooling algorithm based on an improved action with scale invariant instanton solutions, which needs no monitoring or calibration and has a inherent cut off for dislocations. We present results for SU(2) Yang-Mills theory where the method provides good susceptibility data and physical size distributions of instantons.Comment: 3 pages, 4 figures. Talk presented at LATTICE96(topology

Improved cooling algorithm for gauge theories

We propose and study a ``gold-washing" - type of algorithm which smooths out the short range fluctuations but leaves invariant instantons above a certain size. The algorithm needs no monitoring or calibration.Comment: Latex file, 4 pages, 4 figures in uuencoded compressed tar file. Contribution to Lattice 9

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

We measure the running of the $SU(\infty)$ 't Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU($N$) 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 $\tilde l = l \sqrt{N}$, with $l$ the torus period. We set the scale for the running coupling in terms of $\tilde l$ and use the gradient flow to define a renormalized 't Hooft coupling $\lambda(\tilde l)$. 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 $N$ limit taken at fixed value of $\lambda(\tilde l)$. The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at $N =\infty$. 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

A simple algorithm for the estimation of road traffic space mean speeds from data available to most management centres

[Abstract:] The control of the evolution of road traffic streams is highly related to productivity, safety, sustainability and, even, comfort. Although, nowadays, the findings from research efforts and the development of new technologies enable accurate traffic forecasts in almost any conditions, these calculations are usually limited by the data and the equipment available. Most traffic management centres depend on the data provided, at best, by double-loop detectors. These loops supply time means over different aggregation periods, which are indiscriminately used as the bases for subsequent estimations. Since space mean speeds are those needed in most applications (note the fundamental relationship between flow and density in traffic flow theory), most current practice begins with an error. This paper introduces a simple algorithm that the allows estimation of space mean speeds from the data provided by the loops without the need for any additional financial outlay, as long as the traffic in each time interval of aggregation is stationary and its speed distribution is log-normal. Specifically, it is focused on the calculation of the variance of the speeds with regard to the time mean, thus making possible to use the relationship between time mean speeds and space mean speeds defined by Rakha (2005). The results obtained with real data show that the algorithm behaves well if the calculation conditions help fulfil the initial hypotheses. The primary difficulties arise with transient traffic and, in this case, other specific methodologies should be used. Data fusion seems promising in this regard. Nevertheless, it cannot be denied that the improvement provided by the algorithm turns out to be highly beneficial both when used alone in the case of stationarity or as a part of a fusion

Mass anomalous dimension of Adjoint QCD at large N from twisted volume reduction

In this work we consider the $SU(N)$ gauge theory with two Dirac fermions in the adjoint representation, in the limit of large $N$. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of $N$ up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.Comment: 17 pages, 11 figures. Version to appear in JHEP - corrected typos and reference