Wilson loops for U(4) and SU(4) lattice gauge theories in four dimensions

Monte Carlo simulations are used to calculate Wilson loops for pure U(4) and SU(4) gauge theories on a 6⁴ lattice. The first-order phase transitions previously observed in the average action per plaquette for U(4) and SU(4) is also seen in the string tension. U(4) and SU(4) color seem to be confined while U(4) charge in U(4) appears to be deconfined.     

Roughening transition in lattice gauge theories in arbitrary dimension: (II). The groups Z3, U(1), SU(2), SU(3)

Strong coupling expansions for the string tension and other quantities in lattice gauge theories are computed in arbitrary dimension for the groups Z₃, U(1), SU(2), SU(3). This enables us to determine the location of the roughening transition, which seems to be group independent when measured in an appropriate variable. In four dimensions, the strong coupling expansion of string tension calculated up to fourteenth order for SU(2), and twelfth order for SU(3) agrees nicely with Monte Carlo data up to the roughening point.     

U(3) four-dimensional lattice gauge theory and Monte Carlo calculations

Monte Carlo results for the pure U(3) lattice gauge theory on a 6⁴ lattice are reported. Wilson loops and the string tension are presented. The first-order phase transition in U(3) is reflected quite clearly in a discontinuity in the string tension at β = β_c. The U(1) factor of U(3) is extracted using the determinant of the Wilson loops. As expected, the U(1) component appears to deconfine at the phase transition..     

Stochastic confinement and dimensional reduction (II). Three-dimensional SU(2) lattice gauge theory

We study 3-dimensional SU(2) lattice gauge theory with respect to dimensional reduction. By Monte Carlo calculations we find that this reduction is valid to a good approximation (within ≈10%). The adjoint string tension is found to scale approximately. We also compare the adjoint string tension with a string theory.     

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.     

Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.     

Strong coupling expansions for the string tension at finite temperature

The SU(2) euclidean lattice gauge theory is formulated at finite temperature. Previous hamiltonian derivations of the deconfining phase transition are reproduced in the euclidean formalism. Corrections to infinite coupling are calculable, and expansions for the string tension are obtained. It is shown that the string tension is always in a rough phase for any non-zero temperature. The zero in the string tension is therefore trustworthy in the strong coupling regime. Using these results and comparing them with Monte Carlo simulations yields an estimate for the critical temperature of about 230 MeV.     

Compact QED with an extended lattice action

A Monte Carlo study of the compact 4-dimensional U(1) lattice gauge theory with a two-parameter generalization of the Wilson action is presented. The transitions separating confined photons from the spin-wave phase are found to be either first or second order. We measure the correlation length index ν for two second-order critical points on transition lines that do not pass through the usual Wilson action critical point. The agreement between these measurements and previous measurements for the Wilson action tests universality. An argument is given why an SU(N) theory with a similar action might not have a phase diagram like the one for U(1).     

Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g^?24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z₂ in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.     

Analytical Calculations of Large Wilson Loop Averages and String Tension in SU(2) Lattice Gauge Theory

Based on. the Schwinger-Dyson equation for a Wilson loop in the SU(2) lattice gauge theory, we evaluate approximately the averages of Wilson loop of size I × J, from which string tension of the theory has been extracted.     

Monte Carlo studies of wilson loops in four-dimensional U(2) gauge theory

Wilson loops are calculated using Monte Carlo simulations for pure U(2) gauge theory on a 6⁴ lattice. The loops appear to contain an area law piece in both the high and low temperature regions. The string tension is discontinuous at β = β_c, where β_c is the critical inverse temperature. This suggests that the first-order phase transition in U(2) gauge theory is not a deconfining phase transition. The determinant of the Wilson loop, however, extracts the U(1) part of the theory and appears to lose the area law at low temperature.     

Extracting glueball masses from lattice QCD

A general transfer matrix approach to extracting bound-state masses from lattice field theory is presented. Applications are made to SU(2) and SU(3) pure gauge theories. Employing a source of variable strength in the Monte Carlo simulation provides an efficient technique. The lowest mass glueball is found to have a mass of 1.0 ± 0.3 GeV, consistent with other evaluations.     

SU(2)格点规范理论中的重夸克相互作用力及势的计算

本文用Monte Carlo方法对四维对称格点规范理论中具有较好标度性行为的单元格EXP作用量计算了重夸克-反夸克势。计算中利用了重整化群处理方法和SU(2)群的正二十面体子群近似。计算结果与维象的弦理论给出的库仑势加线性势的形式一致。 关键词：     

SU (2) lattice gauge theory and Monte Carlo calculations

Monte Carlo results for theSU (2) lattice gauge theory in four dimensions are presented. The string tension is measured with high statistics and also the mass of the perimeter term is determined. Wilson loop-plaquette correlations, which are related to roughening, are measured.     

Excited glueball states in four-dimensional SU(3) lattice gauge theory

For SU(N) (N ? 2) lattice gauge theories in four dimensions we construct all irreducible representations of the full cubic group on spacelike Wilson loop operators up to length 6. Relying on this set of operators preliminary Monte Carlo results for SU(3) excited glueball states are reported.     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

Some approximate calculations in SU(2) lattice mean field theory

Approximate calculations are performed for small Wilson loops of SU(2) lattice gauge theory in the mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed.     

High-temperature expansions for the free energy of vortices and the string tension in lattice gauge theories

We derive high-temperature cluster expansions for the free energy of vortices in SU(2) and Z₂ lattice gauge theories in 3 and 4 dimensions. The expected behaviour of the vortex free energy is verified. It obeys an area law behaviour. The coefficient of the area is shown to be equal to the string tension between static quarks. We calculate its expansion up to 12th order. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling.     

Universality of the string picture in lattice gauge systems

We test the conjecture that the infrared behaviour of gauge theories is described by an effective string picture by analyzing the Monte Carlo data of five different three- and four-dimensional lattice gauge systems, SU(2) and SU(3) included. We find that there is a unique string of fermionic type which fits well to the whole set of analyzed data.     

SU(2) lattice gauge theory: Standard action versus Symanzik's tree-improved action

We carry out Monte Carlo simulations of the 4d SU(2) lattice gauge theory. The standard action and the Symanzik tree-improved action are used. Results for the string tension, glueball masses, and energy-momentum dispersion are reported. In case of the standard action our results are a finite size study extending previous investigations.Dedicated to the memory of Kurt SymanzikSupported by Deutsche Forschungsgemeinschaft