Improving meson two-point functions by low-mode averaging

Some meson correlation functions have a large contribution from the low lying eigenmodes of the Dirac operator. The contribution of these eigenmodes can be averaged over all positions of the source. This can improve the signal in these channels significantly. We test the method for meson two-point functions.Comment: Talk given at Lattice2004(spectrum), Fermilab, June 21-26, 200

Improving meson two-point functions in lattice QCD

We describe and test a method to compute Euclidean meson two-point functions in lattice QCD. The contribution from the low-lying eigenmodes of the Dirac operator is averaged over all positions of the quark sources. The contribution from the higher modes is estimated in the traditional way with one or a few source points per lattice. In some channels, we observe a significant improvement in the two-point functions for small quark masses.Comment: 10 pages, 7 figure

Instanton Content of the SU(3) Vacuum

We study the topological content of the SU(3) vacuum using the renormalization group (RG) mapping method. RG mapping is a simple smoothing algorithm, in which a series of APE-smearing steps are done while the topological content of the configuration is carefully monitored. This monitoring process makes it possible to separate true topological objects from vacuum fluctuations and allows an extrapolation to zero smearing steps. Using RG mapping we have measured the instanton distribution and topological susceptibility for SU(3) gauge theory. We arrive at a value for the topological susceptibily, ${\chi}^{1/4}$ of 203(5) MeV. The size distribution peaks at $\rho=0.3$fm, and is in good agreement with the prediction of instanton liquid models.Comment: 12 pages, 4 figure

The fixed point action of the Schwinger model

We compute the fixed point action for the Schwinger model through an expansion in the gauge field. The calculation allows a check of the locality of the action. We test its perfection by computing the 1-loop mass gap at finite spatial volume.Comment: 3 pages, LaTeX, 2 figures, uses styles [twoside,fleqn,espcrc2, epsfig], talk presented at Lattice 9

Prospects for perfect actions

The fixed-point (FP) action in QCD, although it is local and determined by classical equations, is difficult to parametrize well and is expensive to simulate. But the stake is high: the FP action has scale invariant instanton solutions, has no topological artifacts, satisfies the index theorem on the lattice, does not allow exceptional configurations, requires no tuning to get the pion massless and is expected to reduce the cut-off effects significantly. An overview is given including a discussion on tests in Yang-Mills theory, QCD and $d=2$ spin and gauge models.Comment: 6 pages, Late

Instanton Effects in Hadron Spectroscopy Revisited

We use an optimised clover action to study spectroscopy on an instanton ensemble reconstructed from smoothed Monte Carlo configurations. Due to the better chirality of the clover action, the artificial configurations show a marked difference from the free field behaviour obtained with the Wilson action. They however still fail to reproduce the physics observed on the smoothed configurations. The presence of freely propagating quark modes is found to be responsible for this.Comment: 3 pages, LaTeX with 4 eps figures, LATTICE99(topology

Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions

The observed slow running of the gauge coupling in SU(3) lattice gauge theory with two flavors of color sextet fermions naturally suggests it is a theory with one relevant coupling, the fermion mass, and that at zero mass correlation functions decay algebraically. I perform a finite-size scaling study on simulation data at two values of the bare gauge coupling with this assumption and observe a common exponent for the scaling of the correlation length with the fermion mass, y_m ~ 1.5. An analysis of the scaling of valence Dirac eigenvalues at one of these bare couplings produces a similar number.Comment: 23 pages, revtex, 13 figure

Perfect Lattice Topology: The Quantum Rotor as a Test Case

Lattice actions and topological charges that are classically and quantum mechanically perfect (i.e. free of lattice artifacts) are constructed analytically for the quantum rotor. It is demonstrated that the Manton action is classically perfect while the Villain action is quantum perfect. The geometric construction for the topological charge is only perfect at the classical level. The quantum perfect lattice topology associates a topological charge distribution, not just a single charge, with each lattice field configuration. For the quantum rotor with the classically perfect action and topological charge, the remaining cut-off effects are exponentially suppressed.Comment: 12 pages, including two figures. ordinary LaTeX, requires fps.sty; Submitted to Phys. Lett.