Computation of the string tension in three dimensional Yang-Mills theory using large N reduction

We numerically compute the string tension in the large N limit of three dimensional Yang-Mills theory using Wilson loops. Space-time loops are formed as products of smeared space-like links and unsmeared time-like links. We use continuum reduction and both unfolded and folded Wilson loops in the analysis.Comment: 13 pages, 10 figures, 2 tables, minor changes to the tex

Topology and Chiral Symmetry in QCD with Overlap Fermions

We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement it numerically. Finally, we give some examples of quenched calculations of chiral symmetry breaking and topology with overlap fermions.Comment: 12 pages with 6 ps figures; crckapb.sty included; to appear in the proceedings of the workshop "Lattice Fermions and Structure of the Vacuum", Oct 5-9, Dubna, Russi

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments we show that the critical exponent $\nu$ describing the vanishing of the physical mass at the critical point is equal to $\nu_\theta/ d_w$. $d_w$ is the Hausdorff dimension of the walk. $\nu_\theta$ is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case of O(N) models, we show that $\nu_\theta=\varphi$, where $\varphi$ is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is $\varphi/\nu$ for O(N) models.Comment: 11 pages (plain TeX

Absence of Physical Walls in Hot Gauge Theories

This paper shows that there are no {\em physical} walls in the deconfined, high-temperature phase of $Z(2)$ lattice gauge theory. In a Hamiltonian formulation, the interface in the Wilson lines is not physical. The line interface and its energy are interpreted in terms of physical variables. They are associated with a difference between two partition functions. One includes only the configurations with even flux across the interface. The other is restricted to odd flux. Also, with matter present, there is no physical metastable state. However, the free energy is lowered by the matter. This effect is described in terms of physical variables.Comment: 25 pages, Revte

Topology and chiral symmetry in finite temperature QCD

We investigate the realization of chiral symmetry in the vicinity of the deconfinement transition in quenched QCD using overlap fermions. Via the index theorem obeyed by the overlap fermions, we gain insight into the behavior of topology at finite temperature. We find small eigenvalues, clearly separated from the bulk of the eigenvalues, and study the properties of their distribution. We compare the distribution with a model of a dilute gas of instantons and anti-instantons and find good agreement.Comment: 3 pages with 3 ps figures; to appear in the proceedings of Lattice '99, Pisa, Italy, June 29 -- July 3, 1999. LATTICE99(topology

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