Phase of the Wilson Line

This paper discusses the global $Z(N)$ symmetry of finite-temperature, $SU(N)$, pure Yang-Mills lattice gauge theory and the physics of the phase of the Wilson line expectation value. In the high $T$ phase, $\langle L \rangle$ takes one of $N$ distinct values proportional to the $Nth$ roots of unity in $Z(N)$, and the $Z(N)$ symmetry is broken. Only one of these is consistent with the usual interpretation $\langle L \rangle = e^{-F/T}$. This relation should be generalized to $\langle L \rangle = z e^{-F/T}$ with $z \in Z(N)$ so that it is consistent with the negative or complex values. In the Hamiltonian description, the {\em physical} variables are the group elements on the links of the spatial lattice. In a Lagrangian formulation, there are also group elements on links in the inverse-temperature direction from which the Wilson line is constructed. These are unphysical, auxiliary variables introduced to enforce the Gauss law constraints. The following results are obtained: The relation $\langle L \rangle=ze^{-F/T}$ is derived. The value of $z \in Z(N)$ is determined by the external field that is needed for the infinite-volume limit. There is a single physical, high-temperature phase, which is the same for all $z$. The global $Z(N)$ symmetry is not physical; it acts as the identity on all physical states. In the Hamiltonian formulation, the high-temperature phase is not distinguished by physical broken symmetry but rather by percolating flux.Comment: 24 pages, no figures, Latex/Revtex 3, UCD-94-2

Numerical results from large N reduced QCD_2

Some results in QCD_2 at large N are presented using the reduced model on the lattice. Overlap fermions are used to compute meson propagators.Comment: 3 pages, contribution to Lattice 2002, Bosto

Remarks on the discretization of physical momenta in lattice QCD

The calculation on the lattice of cross--sections, form--factors and decay rates associated to phenomenologically relevant physical processes is complicated by the spatial momenta quantization rule arising from the introduction of limited box sizes in numerical simulations. A method to overcome this problem, based on the adoption of two distinct boundary conditions for two fermions species on a finite lattice, is here discussed and numerical results supporting the physical significance of this procedure are shown.Comment: 3 pages, 2 figures, Talk presented at Lattice2004(spectrum

Critical Exponent for the Density of Percolating Flux

This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by gauge theory and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the ordered phase of the Ising model and the high temperature, deconfined phase of the gauge theory. The flux picture will be used in this phase. Near the transition, the density is low enough so that flux variables remain useful. There is a finite density of finite flux clusters on both sides of the phase transition. In the deconfined phase, there is also an infinite, percolating network of flux with a density that vanishes as $T \rightarrow T_{c}^{+}$. On both sides of the critical point, the nonanalyticity in the total flux density is characterized by the exponent $(1-\alpha)$. The main result of this paper is a calculation of the critical exponent for the percolating network. The exponent for the density of the percolating cluster is $\zeta = (1-\alpha) - (\varphi-1)$. The specific heat exponent $\alpha$ and the crossover exponent $\varphi$ can be computed in the $\epsilon$-expansion. Since $\zeta < (1-\alpha)$, the variation in the separate densities is much more rapid than that of the total. Flux is moving from the infinite cluster to the finite clusters much more rapidly than the total density is decreasing.Comment: 20 pages, no figures, Latex/Revtex 3, UCD-93-2

Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge Theory

We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of SU(2) gauge theory. To this end we carefully study the corrections to the scaling functions of the observables coming from irrelevant exponents. As a guiding line for determining the critical amplitudes we use envelope equations derived from the finite size scaling formulae for the observables. The equations are then evaluated with new high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find different correction-to-scaling behaviours above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d Ising model.Comment: LATTICE98(hightemp