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.
16594164
Low-lying fermion modes: Dynamical versus quenched
Abstract We compare the low-lying eigenmodes of the O(a) improved Wilson-Dirac operator on quenched and dynamical configurations and investigate methods of probing the topological properties of gauge configurations.
17614040
Unquenching the topological susceptibility with an overlap action
Abstract We estimate the quark-mass dependence of the topological susceptibility with dynamical overlap and clover fermions. Unquenching effects on the susceptibility turn out to be well approximated by a reweighting of a quenched ensemble with a low-eigenmode truncation of the fermionic determinant. We find that it is most likely due to the explicit chiral symmetry breaking of the fermion action that present day dynamical simulations do not show the expected suppression of the topological susceptibility.
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.
119244858
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.
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.
117844992
Instantons and Fermions on the Lattice
I address the question of how much of QCD in the chiral limit is reproduced by instantons. After reconstructing the instanton content of smoothed Monte Carlo lattice configurations, I compare hadron spectroscopy on this instanton ensemble to the spectroscopy on the original “physical” smoothed configurations using a chirally optimised clover fermion action. Instantons by themselves are shown to break chiral symmetry but hadron correlators on the instanton backgrounds are strongly influenced by free quark propagation. This results in unnaturally light hadrons and a small splitting between the vector and the pseudoscalar meson channels. Superimposing a perturbative ensemble of zero momentum gauge field fluctuations on the instantons eliminates the free quarks and restores the physical hadron correlators. I argue that the torons that are present only in finite volumes, are probably needed to compensate the unnaturally large finite size effects due to the lack of confinement in the instanton ensemble.
17320381
Revealing topological structure in the SU(2) vacuum
Abstract In this paper we derive a simple parametrization of the cycling method developed by us in our earlier work. The new method, called renormalization group (RG) mapping, consists of a series of carefully tuned APE-smearing steps. We study the relation between cycling and RG mapping. We also investigate in detail how smooth instantons and instanton-anti-instanton pairs behave under the RG mapping transformation. We use the RG-mapping technique to study the topological susceptibility and instanton size distribution of SU(2) gauge theory. We find scaling in both quantities in a wide range of coupling values. Our result for the topological susceptibility, χ 1 4 = 220(6) MeV , agrees with our earlier results.
120060029
Tensor force and Debye screening in quarkonium-type mesons
We use a non-relativistic quantum-mechanical model to investigate the effect of a screening plama on two quarkonium-type mesons: the charmonium and the bottonium. The stability of these mesons in the plasma is estimated in two cases: including the tensor and spin-orbit term in the potential and without these terms. It turns out that while the bottonium is somewhat stabilized by the tensor force, the charmonium becomes less stabil due to this modification of the potential. Thus the charmonium seems to be a more sensitive probe of the quark-gluon plasma formation than it was thought to be without including the tensor force.
207778110
Optimizing the Chiral Properties of Lattice Fermions