20001314
Topological structure in the SU(2) vacuum
We study the topological content of the vacuum of SU(2) pure gauge theory using lattice simulations. We use a smoothing process based on the renormalization group equation which removes short distance fluctuations but preserves long distance structure. The action of the smoothed configurations is dominated by instantons, but they still show an area law for Wilson loops with a string tension equal to the string tension on the original configurations. Yet it appears that instantons are not directly responsible for confinement. The average radius of an instanton is about 0.2 fm, at a density of about 2 fm 4 . This is a much smaller average size than other lattice studies have indicated. The instantons appear not to be randomly distributed in space, but are clustered.
121462735
The phase structure of two-dimensional pure lattice gauge theories with Chern term
We study the phase structure of two-dimensional pure lattice gauge theories with Wilson plus Chern action. Since the Chern term is purely imaginary it introduces a rich phase structure compared to the originally trivial Wilson model. The Zn model is considered in detail and it is proved that for n > 2 it has an infinite number of first order phase transitions. Confinements is maintained in pure phases but at the phase transition points the string tension vanishes for certain charges.
53865786
Monopoles and instantons in SU(2) lattice gauge theory
Abstract We investigate the monopole-instanton correlation in SU(2) lattice gauge theory using a renormalisation group inspired smoothing technique. We look at the properties of monopole clusters and their correlation with instantons. Since the action of the smoothed configurations is dominated by instantons we compare the smoothed Monte Carlo lattices to artificially reconstructed configurations with the same instanton content but no other fluctuations. Both parallel and randomly rotated (in group space) instanton ensembles are considered.
9446326
Some remarks on Abelian dominance
Abstract We used a renormalisation group based smoothing to address two questions related to abelian dominance. smoothing enable us to extract the abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov gauge projected abelian configurations do not have a consistent physical meaning. We also applied the smoothing on SU(2) configurations to test how sensitive abelian dominance in the maximal abelian gauge is to the short distance fluctuations. We found that on smoothed SU(2) configurations the abelian string tension was about 30% smaller than the SU(2) string tension which was unaffected by smoothing. This suggests that the approximate abelian dominance found with the Wilson action is probably an accident and it has no fundamental physical relevance.
118422773
Z(2) Excitations and Disorder in SU(2) Spin Models and Gauge Theories.
16990128
SO (3) vortices as a mechanism for generating a mass gap in the 2D SU (2) principal chiral model
Abstract We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external Z (2) flux introduced by twisted boundary conditions. This condition in turn is rewritten in terms of an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a non-zero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a non-zero effective magnetic field. Finally, we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.
16458442
Locality and topology with fat link overlap actions
We study the locality and topological properties of fat link clover overlap (FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1 step of HYP) already results in greatly improved properties compared to the Wilson overlap (WO). We present a detailed study of the localisation of the FCO and its connection to the density of low modes of $A^\dagger A$. In contrast to the Wilson overlap, on quenched gauge backgrounds we do not find any dependence of the localization of the FCO on the gauge coupling. This suggests that the FCO remains local in the continuum limit. The FCO also faithfully reproduces the zero mode wave functions of typical lattice instantons, not like the Wilson overlap. After a general discussion of different lattice definitions of the topological charge we also show that the FCO together with the Boulder charge are likely to satisfy the index theorem in the continuum limit. Finally, we present a high statistics computation of the quenched topological susceptibility with the FCO action.
117909068
High temperature quark localization by Polyakov loops
We study the low eigenmodes of the overlap and staggered Dirac operator at high temperature. We show that the recently found localized quark modes obeying Poisson statistics are connected to physical gauge field objects with their size and density scaling in the continuum limit. The localized modes are also strongly correlated with large fluctuations of the Polyakov loop. Based on that we construct a random matrix model of the low Dirac modes inspired by dimensional reduction. Our model reproduces the Poisson to random matrix transition seen in the lattice Dirac spectrum.
118554181
Poisson Statistics in the High Temperature QCD Dirac Spectrum
At low temperature in the epsilon regime of QCD the low-end of the Dirac spectrum is described by random matrix theory. In contrast, there has been no similarly well established staistical description in the high temperature, chirally symmetric phase. Using lattice simulations we show that at high temperature a band of extremely localized eigenmodes appear at the low-end of the Dirac spectrum. The corresponding eigenvalues are statistically independent and obey a generalized Poisson distribution. Higher up in the spectrum the Poisson distribution rapidly crosses over into the bulk distribution predicted by the random matrix ensemble with the corresponding symmetry. Our results are based on quenched lattice simulations with the overlap and the staggered Dirac operator done well above the critical temperature at several volumes and values of $N_t$. We also discuss the crucial role played by the fermionic boundary condition and the Polyakov-loop in this phenomenon.
15393945
Gapless Dirac spectrum at high temperature
Using the overlap Dirac operator I show that, contrary to some expectations, even well above the critical temperature there is not necessarily a gap in the Dirac spectrum in pure SU(2) gauge theory. This happens when the Polyakov loop and the fermion boundary condition combine to give close to periodic boundary condition for the fermions in the time direction. In this Polyakov loop sector there is a non-vanishing density of Dirac eigenvalues around zero which implies that chiral symmetry is spontaneously broken. I demonstrate this both directly and also by finding good agreement with the random matrix theory prediction for the distribution of the lowest Dirac eigenvalue. I show that the chiral condensate increases with the tempereture therefore it is very unlikely to be explained by topological fluctuations that become rapidly smaller above Tc. Finally I show that it is only a small fraction of the lowest Dirac eigenvalues that decide which Polyakov loop sector is favored by the fermion determinant if dynamical fermions are turned on. This provides a qualitative understanding of how the loss of confinement above Tc implies the restoration of chiral symmetry.
14910940
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 lattice simulations with the SU(2) gauge group.