The free energy of higher representation sources in lattice gauge theories

Deconfinement of higher representation sources in SU(2) lattice gauge theory is studied by a Monte Carlo simulation on an 8³×2 lattice. Results for the free energy are compared with expectations from the effective theory of thermal Polyakov loops, and critical exponents for the magnetization of different representations in SU(2) are computed. We also compare the predictions for higher representations in SU(3) lattice gauge theory with some recent Monte Carlo data. Finally, possible phenomenological consequences of the deconfinement associated with higher representation sources are discussed.     

String tensions of SU(3) gauge theory on a random lattice

The SU(3) gauge theory on a random lattice is studied using the Monte Carlo method. The string tensions are measured. A scaling window around g₀⁻² = 1.4 is detected and the scale parameter is estimated.     

The interquark potential: SU(2) colour gauge theory with fermions

Including dynamical fermions in the Monte Carlo simulation of the SU(2) gauge theory, the potential between static quarks is investigated on a 16×8³ lattice. The Coulomb part of the force is stronger as compared with the pure gauge field theory. At large distances indications are found for a deviation from the linear rise of the potential, expected from a break-up of the flux tube between the heavy quarks through spontaneous creation of light quark pairs.     

The string tension and the scaling behavior of SU(2) gauge theory on a random lattice

The SU(2) gauge theory on an 8⁴ random lattice has been studied by the Monte Carlo method. The string tensions have been evaluated. They display the expected scaling behavior for β=1.2−1.3. The scale parameter Λ_RAN has been determined approximately.     

Modified action glueballs

The mass of the 0⁺ glueball in 4-dimensional lattice gauge theory with a mixed SU(2)-SO(3) action is obtained via Monte Carlo. We work in a region far from the critical end point in the phase diagram, with an action partly motivated by renormalization group flows in the Migdal-Kadanoff approximation. A large-N resummation of perturbation theory is used to show that the mass gap scales as predicted by the perturbative renormalization group. Independent of this, our results show that the ratio of the glueball mass to the square root of the string tension, obtained from a previous Monte Carlo, is a renormalization group invariant.     

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.     

Monte Carlo variational study of glueball masses in SU (2) lattice gauge theory for coupling less than one

A Monte Carlo variational calculation of glueball masses is performed in SU (2) lattice gauge theory for coupling less than 1. The preliminary upper bounds are obtained, on a 4³×8 lattice, M(0⁺)=1.38±0.26 GeV, M(2⁺)=1.39±0.41 GeV. Evidence of the existence of differences from the results for g²> 1 is observed.     

Monte Carlo calculation of SU(2) glueball states with Symanzik's tree-level improved action

With the tree-level improved 4d SU(2) lattice gauge theory we carry out a Monte Carlo calculation of the spectrum. We find a scaling window for the 0⁺ state, leading to m(0⁺) ≈ 53 Λ^TI_L. Results for the 2⁺ state are somewhat inconclusive but also consistent with scaling.     

Complex singularities in the specific heat of the SU(2) lattice gauge model

A recent Monte Carlo simulation showing a sharp peak versus β in the specific heat for an SU(2) lattice gauge theory is compared with the high temperature expansion. An interpretation based on complex β-plane singularities is proposed.     

Density ofZ(3) flux loops inSU(3) lattice gauge theory in four dimensions

A mixed actionSU(3)-SU(3)/Z(3) gauge theory is simulated by Monte Carlo methods on a 4⁴ lattice. The density ofZ(3) flux loops is measured.     

Higgs and W mass on the lattice at strong gauge coupling

At infinite gauge coupling the gauge fields in the fundamental lattice SU(N) Higgs model can be integrated out exactly. In the resulting effective theory of the radial Higgs field we derive a string -like correlation function that represents the leading behavior of the W two-point function at small β. For large N we then compute the W-mass and the Higgs mass. These analytical results are qualitatively similar to what has been found in Monte Carlo simulations of the SU(2) model.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

A phase transition in SU(5) lattice gauge theory in four dimensions

Monte Carlo simulations of the average action per plaquette are calculated for four-dimensional SU(5) gauge theory on a 3⁴ lattice. Evidence is found for a discontinuity in this order parameter which is a signal for a first-order phase transition.     

More evidence for universality in the SU(2) lattice gauge theory

The O⁺ glueball mass in the fundamental-adjoint SU(2) la ttice gauge theory is extracted from the Monte Carlo data on the correlation functions at time distances t = 1 and t = 2 on a 8⁴ lattice. The ratio $\text{m}{}_{\mathrm{<mtext>g</mtext>}}\text{σ}$ is constant in the β_F ?β_A region explored giving more evidence in favour of the universality hypothesis.     

SU(2) string tension,glueball mass and interquark potential by Monte Carlo computations

Monte Carlo simulations of the SU(2) gauge system on a large (16⁴) lattice and with high statistics are performed to determine several quantities of physical interest. Previous evaluations of the ratio between string tension, σ, and scale constant, Λ₀, are confirmed. The mass of the glueball is found to be approximately 3√σ and the potential between static charges at very small separation is 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.     

String tension in SU(3) lattice gauge theory

Wilson loop expectation values have been determined in SU(3) lattice gauge theory without fermions using Monte Carlo methods and considering lattices of up to 10⁴ sites. A heat bath technique has been developed in order to enhance the statistical independence of successive lattice configurations.     

The glueball mass spectrum in QCD: First results of a lattice Monte Carlo calculation

We perform a variational calculation of the masses of glueballs of various spins and parities in SU(2) gauge theory. The quantum vacuum we use is generated by the lattice Monte Carlo technique. Our first results, obtained on medium sized lattices give m(0⁺) = (3.6 ± 0.35) Λ_mom, m(0^? = (6.0 ± 1.0)Λ_mom, m(2⁺) = (6.5^+1.8_?1.1)Λ_mom, various mass upper bounds and information on glueball wave functions.     

Monte Carlo simulation of SU(2) gauge theory with fermions on a four-dimensional lattice

After integration over the fermions in an SU(2) lattice gauge theory, the effective fermionic action may be expressed as a sum over all possible closed gauge field loops with corresponding weight factors. We approximate this sum and perform a Monte Carlo simulation of a coupled fermion-gauge system on a 4⁴ lattice. We compare our results for 〈S_eff〉 and $\text{〈}\text{ψ}\text{ψ〉}$ for different values of the gauge field coupling β and fermion coupling κ with the free fermion theory on a lattice. 〈S_eff〉 turns out to be quite small for $\text{κ?}\text{1}\text{8}$.