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.
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.
15253180
Pentaquark hadrons from lattice QCD
We study spin 1/2 isoscalar and isovector candidates in both parity channels for the recently discovered ?+ (1540) pentaquark particle in quenched lattice QCD. Our analysis takes into account all possible uncertainties, such as statistical, finite size and quenching errors when performing the chiral and continuum extrapolations and we have indications that our signal is separated from scattering states. The lowest mass that we find in the IP = 0? channel is in complete agreement with the experimental value of the ?+ mass. On the other hand, the lowest mass state in the opposite parity IP = 0+ channel is much higher. Our findings suggests that the parity of the ?+ is negative.
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.
15028871
Pentaquark search with spatially non-trivial operators (II)
We study spin 1/2 isoscalar and isovector, even and odd parity candidates for the Θ + (1540) pentaquark particle using large scale lattice QCD simulations. Two complications extracting the lowest state in a given parity channel are studied. Firstly, we summarize how the energy of the lowest state can be extracted separately in the two parity channels. Secondly, after summarizing the relevant group theoretical principles we discuss how spin 1/2 pentaquark operators can be constructed.
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.
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.
118902859
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.
125260415
Homology and abelian lattice gauge theories
A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.
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.
123308488
The effect of pion condensation on superfluidity in neutron stars
The authors study the effect of pion condensation on the energy gap of superfluid neutron matter. The neutron energy spectrum is determined in a Walecka-type model in the mean-field approximation. This spectrum is inserted into the BCS model to calculate the energy gap for singlet pairing superfluid neutron matter. With this procedure they calculate the energy gap for pion condensed and normal matter at various densities. It turns out that in the superfluid density region the pion condensation is too weak to modify the energy gap significantly.