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.
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.
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.
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.
117786356
Exotic baryons on the lattice
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.
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.
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.