119443613
Instantons and chiral symmetry 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 optimized clover fermion action. By studying the zero mode zone in simple instances I find that the optimized action gives a satisfactory description of it. Through the Banks-Casher formula, 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 (torons) on the instantons is found to be enough to eliminate the free quarks and restore 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.
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.
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.
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.
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.
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.
125995373
The topological susceptibility with dynamical overlap fermions
119392327
Improving the chiral properties of lattice fermions
The chiral properties of lattice fermions can be improved by altering either their fermion-gauge coupling or the pure gauge part of the action (or both). 
Using both perturbation theory and nonperturbative simulation, we compare a simple alteration of the gauge action (which encompasses the Wilson, Symanzik, Iwasaki, and DBW2 actions), and HYP-blocked links in the fermion action. Perturbative tests include calculations of the potential, flavor-changing quark scattering amplitudes, and matching factors for currents. Non-perturbative tests include the potential, measurements of flavor symmetry breaking for staggered fermions, the behavior of topological objects, and properties of overlap actions. Our results display the bad properties of these actions as well as their good ones.
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.
12447919
Absence of correlations in the QCD dirac spectrum at high temperature.
I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the absence of correlations between different regions of the low-lying spectrum I derive analytic formulas for the distribution of the first two eigenvalues. I find good agreement with data obtained using the overlap Dirac operator in quenched SU(2) lattice simulations. This suggests that if chiral symmetry is restored spectral correlations are not important and all the statistical properties of the spectrum are encoded in the spectral density.