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.
118422773
Z(2) Excitations and Disorder in SU(2) Spin Models and Gauge Theories.
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.
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.
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.
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.
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.
125995373
The topological susceptibility with dynamical overlap fermions
118985245
The Status of Pentaquark Spectroscopy on the Lattice
The present work is a summary of the status of lattice pentaquark calculations. After a pedagogic introduction to the basics of lattice hadron spectroscopy we give a critical comparison of results presently available in the literature. Special emphasis is put on presenting some of the possible pitfalls of these calculations. In particular we discuss at length the choice of the hadronic operators and the separation of genuine five-quark states from meson-baryon scattering states.
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.
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.