Fixed point action and topological charge for SU(2) gauge theory

We present a theoretically consistent definition of the topological charge operator based on renormalization group arguments. Results of the measurement of the topological susceptibility at zero and finite temperature for SU(2) gauge theory are presented.Comment: 3 pages, LaTeX file. Talk presented at LATTICE96(improvement

Comment on ``Evidence Against Instanton Dominance of Topological Charge Fluctuations in QCD''

We comment on the recent paper (hep-lat/0102003) by Horvath, Isgur, McCune, and Thacker, which concludes that the local chiral structure of fermionic eigenmodes is not consistent with instanton dominance. Our calculations, done with an overlap action, suggest the opposite conclusion.Comment: 5 pages, Revtex, 4 postscript figures. COLO-HEP-45

Non--perturbative tests of the fixed point action for SU(3) gauge theory

In this paper (the second of a series) we extend our calculation of a classical fixed point action for lattice $SU(3)$ pure gauge theory to include gauge configurations with large fluctuations. The action is parameterized in terms of closed loops of link variables. We construct a few-parameter approximation to the classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity $G = L \sqrt{\sigma(L)}$ where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L \sigma(L)$. We measure $G$ on lattices of fixed physical volume and varying lattice spacing $a$ (which we define through the deconfinement temperature). While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for $1/2 \ge aT_c \ge 1/6$. Similar behaviour is found for the potential measured in a fixed physical volume.Comment: 28 pages (latex) + 11 figures (Postscript), uuencode

The role of heavy fermions

Heavy dynamical fermions with masses around the cut-off do not change the low energy physics apart from a finite renormalization of the gauge coupling. In this paper we study how light the heavy fermions have to be to cause more than this trivial renormalization.Comment: uuencoded 3 page postscript contribution to Lattice 93, COLO-HEP-33

Perfect Scalars on the Lattice

We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.Comment: 26 pages, 11 figure