Twisted Eguchi-Kawai Model Research Articles

On the deconfining transition of SU(∞) gauge theory

Monte Carlo simulations for twisted Eguchi-Kawai models with asymmetric couplings have been used to investigate the large-N deconfining phase transition of pure SU(N) gauge theories. Data with N = 25, 36, 49 and 64 and the variable asymmetry parameter ξ allow us to disentangle these theories' bulk first-order transition from their physical deconfining transition. The SU(64) data is in good agreement with asymptotic freedom and gives a critical temperature of Tc/ΛE = 1 118 ± 6 or Tc/√σ = 0.42 + 0.05, which is close to the SU(3) ratio of deconfining temperature to the string tension. The data also suggest that the transition is first order.

Weak coupling analysis of the finite-temperature twisted Eguchi-Kawai model

We show that with a suitable twist the finite-temperature twisted Eguchi-Kawai model reproduces the planar perturbation expansion of the full Wilson theory in the weak coupling sector.

Numerical study of Langevin equation in twisted Eguchi-Kawai model

The Langevin equation at the group manifolds is derived and investigated for the twisted Eguchi-Kawai model The numerical results for the string tension for various values of N are combined with the known Monte Carlo results to give an improved value of the string tension. The distribution of eigenvalues of Wilson loop matrices are also studied.

SU (∞) gauge theories on asymmetric lattices

We study SU (∞) gauge theory on an asymmetric lattice using a generalisation of the twisted Eguchi-Kawai model. We show that it is possible to remove the large- N bulk transition by choosing a sufficiently asymmetric lattice and hence to study the physical deconfinement transition without being affected by the former. Results for N = 16 indicate a strong first order deconfinement transition.

Heat bath method for the twisted Eguchi-Kawai model

We reformulate the twisted Eguchi-Kawai model in a way that allows us to use the heat bath method for the updating procedure of the link matrices. This new formulations is more effecient by a factor of 2.5 in computer time and of 2.3 in memory need.

Generalized twisted Eguchi-Kawai models

We introduce classes of twisted reduced models which have identical planar sectors. By taking suitable combinations the planar sector can be extracted. We check the models by Monte Carlo calculations for the two-dimensional twisted Eguchi-Kawai model.

Instantons versus factorization in large- N field theories

We discuss the contribution of surviving extrema for the action in N→ ∞ Yang-Mills theories in weak coupling and their relevance for factorization. In particular we discuss the role of fluxons in the twisted Eguchi-Kawai model.

The deconfinement phase transition at large N: A study of the hot twisted Eguchi-Kawai model

The deconfinement phase transition for SU(54) gauge theory is studied using twisted Eguchi-Kawai methods. Expectation values of the action, the Wilson line and the energy density are measured. We find evidence for deconfining phase transition and compare our data with the naive string picture.

Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU( N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.

Numerical study of the Langevin equation in the twisted Eguchi-Kawai model: Distribution of the eigenvalues of the plaquette matrix

The four-dimensional twisted Eguchi-Kawai model is investigated numerically using the Langevin equation. The results for the plaquette energy agree with those of the known Monte Carlo calculations. The new result is the distribution of the eigenvalues of the plaquette matrix. In the strong coupling phase this distribution is smooth, whereas in the weak coupling phase a gap is clearly seen.

A note on the continuum version of the twisted Eguchi-Kawai model

We give a recipe for large N (gauge and non-gauge) continuum reduced models in even space-time dimensions which preserves the features of the twisted reduced model on the lattice. This prescription leads to a regularized rotationally invariant theory for N = ∞; at the same time the cyclicity in N seems crucial for the reduced gauge models for finite N. Comparison with a recent work on the subject is made.

String tension for large- N gauge theory

The string tension for large- N gauge theory is evaluated by performing Monte Carlo simulations of the recently proposed twisted Eguchi-Kawai model. The Large- N Yang-Mills theory is shown to be a confining, asymptotically free theory.

Numerical analysis of the twisted Eguchi-Kawai model in two dimensions

Using Monte Carlo methods we compare the twisted Eguchi-Kawai model for several N values with the SU(∞) lattice gauge theory in two dimensions. We find agreement only for loops with smaller then N 2. So the twisted Eguchi-Kawai model does not reproduce the SU(∞) lattice gauge theory on a N 2 lattice.

A finite temperature twisted Eguchi-Kawai model

We introduce a finite temperature version of the twisted Eguchi-Kawai model and study it at low temperature via Monte Carlo calculations. The model reproduces the results previously obtained by Gonzalez-Arroyo and Okawa.

The twisted Eguchi-Kawai model fails to reproduce the weak coupling of the wilson model

We perform a saddle point analysis of the twisted Eguchi-Kawai model in two, three and four dimensions. Our conclusion is that this model does not reproduce the usual Wilson model results in the weak coupling region at the large N limit. However, we stress that the deviations between the two models are small and decrease with increasing dimension of space.

Minimizing configurations of the action in the twisted Eguchi-Kawai model

We obtain the most general twist matrix compatible with the minimization condition of the twisted Eguchi-Kawai model. For all values of the twist tensor, we propose configurations of matrices which realize the minimum of the action.