2,030 research outputs found
Absence of confinement in the absence of vortices
We consider the Wilson loop expectation in SU(2) lattice gauge theory in the
presence of constraints. The constraints eliminate from the functional measure
gauge field configurations whose physical interpretation is that of thick
center vortices linking with the loop. We give a simple proof that, for
dimension , the so constrained Wilson loop follows perimeter law,
i.e. non-confining behavior, at weak coupling (low temperature). Thus the
presence of vortex configurations is a necessary condition for confinement.Comment: 14 pages, LaTeX fil
Bound on the string tension by the excitation probability for a vortex
A lower bound on the string tension for large beta in SU(2) LGT is derived.
The derivation is from first principles and bounds the string tension from
below by the expectation for the excitation of a single `tagged' thick vortex
winding around the lattice. Thus confinement follows if this expectation
remains nonvanishing at large beta. Numerical simulations are presented to show
that this is indeed the case.Comment: LATTICE99(confine), 3 pages, 3 epsf figures, LaTeX, espcrc2.st
SO(3) vortices and disorder in the 2d SU(2) chiral model
We study the correlation function of the 2d SU(2) principal chiral model on
the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled
to SO(3) vortices we show that the vortices play a crucial role in disordering
the correlations at low temperature. Using a series of exact transformations we
prove that, if satisfied, certain inequalities between vortex correlations
imply exponential fall-off of the correlation function at arbitrarily low
temperatures. We also present some Monte Carlo evidence that these correlation
inequalities are indeed satisfied. Our method can be easily translated to the
language of 4d SU(2) gauge theory to establish the role of corresponding SO(3)
monopoles in maintaining confinement at small couplings.Comment: 13 pages LaTe
Anderson Localization in Quark-Gluon Plasma
At low temperature the low end of the QCD Dirac spectrum is well described by
chiral random matrix theory. In contrast, at high temperature there is no
similar statistical description of the spectrum. We show that at high
temperature the lowest part of the spectrum consists of a band of statistically
uncorrelated eigenvalues obeying essentially Poisson statistics and the
corresponding eigenvectors are extremely localized. Going up in the spectrum
the spectral density rapidly increases and the eigenvectors become more and
more delocalized. At the same time the spectral statistics gradually crosses
over to the bulk statistics expected from the corresponding random matrix
ensemble. This phenomenon is reminiscent of Anderson localization in disordered
conductors. Our findings are based on staggered Dirac spectra in quenched SU(2)
lattice simulations.Comment: 11 pages, 8 figure
Computation of the Vortex Free Energy in SU(2) Gauge Theory
We present the first measurement of the vortex free-energy order parameter at
weak coupling for SU(2) in simulations employing multihistogram methods. The
result shows that the excitation probability for a sufficiently thick vortex in
the vacuum tends to unity. This is rigorously known to provide a necessary and
sufficient condition for maintaining confinement at weak coupling in SU(N)
gauge theories.Comment: 7 pages, LaTeX with 3 eps figures, minor changes, replacement of Fig.
Poisson to Random Matrix Transition in the QCD Dirac Spectrum
At zero temperature the lowest part of the spectrum of the QCD Dirac operator
is known to consist of delocalized modes that are described by random matrix
statistics. In the present paper we show that the nature of these eigenmodes
changes drastically when the system is driven through the finite temperature
cross-over. The lowest Dirac modes that are delocalized at low temperature
become localized on the scale of the inverse temperature. At the same time the
spectral statistics changes from random matrix to Poisson statistics. We
demonstrate this with lattice QCD simulations using 2+1 flavors of light
dynamical quarks with physical masses. Drawing an analogy with Anderson
transitions we also examine the mobility edge separating localized and
delocalized modes in the spectrum. We show that it scales in the continuum
limit and increases sharply with the temperature.Comment: 10 pages, 9 eps figures, a few references added and typos correcte
Anderson localization through Polyakov loops: lattice evidence and Random matrix model
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures
above the phase transition. Both staggered and overlap spectra reveal
transitions from chaotic (random matrix) to integrable (Poissonian) behavior
accompanied by an increasing localization of the eigenmodes. We show that the
latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong"
Polyakov loops can therefore be viewed as defects leading to Anderson
localization in gauge theories. We find strong similarities in the spatial
profile of these localized staggered and overlap eigenmodes. We discuss
possible interpretations of this finding and present a sparse random matrix
model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added,
some axis labels corrected; journal versio
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