Z(2) vortices and the string tension in SU(2) gauge theory

We exhibit the appropriate variables allowing the plus-minus (Z(2)) `reduction' of the Wilson loop operator which provides a direct measure of the thin, thick and `mixed' Z(2) topological, gauge-invariant vortices in SU(2) LGT. Simulations with the Wilson action, as well as a perfect action smoothing procedure, show the string tension to be reproduced from the contributions of these excitations.Comment: 3 pages, LaTeX, 4 figures, uses espcrc2.sty, Talk given at LATTICE9

Renormalization Group Therapy

We point out a general problem with the procedures commonly used to obtain improved actions from MCRG decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not representative of the equilibrium configurations of the assumed form of the effective action at the measured couplings. Curing this involves fine-tuning of the chosen MCRG decimation procedure, which is also dependent on the form assumed for the effective action. We illustrate this in decimation studies of the SU(2) LGT using Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette improved action involving five group representations and free of this pathology is given.Comment: 18 pages, 9 figures, 9 table

Improving the improved action

We investigate the construction of improved actions by the Monte Carlo Renormalization Group method in the context of SU(2) gauge theory utilizing different decimation procedures and effective actions. We demonstrate that the basic self-consistency requirement for correct application of MCRG, i.e. that the decimated configurations are equilibrium configurations of the adopted form of the effective action, can only be achieved by careful fine-tuning of the choice of decimation prescription and/or action.Comment: 8 pages, 5 figure

RG Decimations and Confinement

We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, $0 < \beta <\infty$, defined at lattice spacing a. The approach employed is to obtain both upper and lower bounds for the partition function and the `twisted' partition function in terms of approximate decimation transformations. The behavior of the exact quantities is thus constrained by that of the easily computable bounding decimations.Comment: 6 pages, 1 figure, latex using espcrc2.sty, presented at `QCD Down Under', Adelaide, Australia, May 10-19, 200

Loop inequalities and confinement

We consider correlation inequalities that follow from the well-known loop equations of LGT, and their analogues in spin systems. They provide a way of bounding long range by short or intermediate range correlations. In several cases the method easily reproduces results that otherwise require considerable effort to obtain. In particular, in the case of the 2-dimensional O(N) spin model, where large N analytical results are available, the absence of a phase transition and the exponential decay of correlations for all $\beta$ is easily demonstrated. We report on the possible application of this technique to the analogous 4-dimensional problem of area law for the Wilson loop in LGT at large $\beta$.Comment: Lattice2002(topology), 3 page