137 research outputs found
Phase of the Wilson Line
This paper discusses the global symmetry of finite-temperature,
, pure Yang-Mills lattice gauge theory and the physics of the phase of
the Wilson line expectation value. In the high phase,
takes one of distinct values proportional to the roots of unity in
, and the symmetry is broken. Only one of these is consistent with
the usual interpretation . This relation should
be generalized to with 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 is derived. The value of 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
. The global 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
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 . On
both sides of the critical point, the nonanalyticity in the total flux density
is characterized by the exponent . 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 . The specific heat exponent and the crossover exponent
can be computed in the -expansion. Since , 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
Adjoint Wilson Line in SU(2) Lattice Gauge Theory
The behavior of the adjoint Wilson line in finite-temperature, ,
lattice gauge theory is discussed. The expectation value of the line and the
associated excess free energy reveal the response of the finite-temperature
gauge field to the presence of an adjoint source. The value of the adjoint line
at the critical point of the deconfining phase transition is highlighted. This
is not calculable in weak or strong coupling. It receives contributions from
all scales and is nonanalytic at the critical point. We determine the general
form of the free energy. It includes a linearly divergent term that is
perturbative in the bare coupling and a finite, nonperturbative piece. We use a
simple flux tube model to estimate the value of the nonperturbative piece. This
provides the normalization needed to estimate the behavior of the line as one
moves along the critical curve into the weak coupling region.Comment: 21 pages, no figures, Latex/Revtex 3, UCD-93-1
Topological Excitations in the Thirring model
The quantization of the massless Thirring model in the light-cone using
functional methods is considered. The need to compactify the coordinate
in the light-cone spacetime implies that the quantum effective action for
left-handed fermions contains excitations similar to abelian instantons
produced by composite of left-handed fermions. Right-handed fermions don't have
a similar effective action. Thus, quantum mechanically, chiral symmetry must be
broken as a result of the topological excitations. The conserved charge
associated to the topological states is quantized. Different cases with only
fermionic excitations or bosonic excitations or both can occur depending on the
boundary conditions and the value of the coupling.Comment: title changed, one reference added, accepted in Phys. Lett.
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
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 describing the vanishing of
the physical mass at the critical point is equal to . is
the Hausdorff dimension of the walk. 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 , where
is the crossover exponent known in the context of field theory. This implies
that the Hausdorff dimension of the walk is for O(N) models.Comment: 11 pages (plain TeX
Large N reduction with overlap fermions
We revisit quenched reduction with fermions and explain how some old problems
can be avoided using the overlap Dirac operator.Comment: Lattice2002(chiral) 3 pages, no figure
Two dimensional fermions in three dimensional YM
Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite .
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table
Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion Electromagnetic Form Factor
We investigate the utility of partially twisted boundary conditions in
lattice calculations of meson observables. For dynamical simulations, we show
that the pion dispersion relation is modified by volume effects. In the isospin
limit, we demonstrate that the pion electromagnetic form factor can be computed
on the lattice at continuous values of the momentum transfer. Furthermore, the
finite volume effects are under theoretical control for extraction of the pion
charge radius.Comment: 15 pages, 8 figures, revisions to text, refs adde
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