Topological Structure in the Su(2) Vacuum * †

We study the topological content of the vacuum of SU (2) pure gauge theory using lattice simulations. We use a smoothing process based on the renormalization group equation. This removes short distance fluctuations but preserves long distance structure. The action of the smoothed configurations is dominated by instantons, but they still show an area law for Wilson loops with an unchanged string tension. The average radius of an instanton is about 0.2 fm, at a density of about 2 fm −4. Based on phenomenological models, it has been argued that instantons are largely responsible for the low energy hadron and glueball spectrum [1]. Instanton liquid models attempt to reproduce the topological content of the QCD vacuum and conclude that hadronic correlators in the instanton liquid show all the important properties of the corresponding full QCD correlators. These models appear to capture the essence of the QCD vacuum , but their derivations involve a number of uncontrolled approximations and phenomenolog-ical parameters. Lattice methods are the only ones we presently have, which might address this connection starting from first principles. Lattice studies of in-stantons can suffer from several difficulties. An unambiguous topological charge can be assigned only to continuous gauge field configurations living on a continuum space-time. On the lattice, the charge can only be defined as that of an interpolated continuum filed configuration. This interpolation however is non-unique on Monte Carlo generated lattice configurations. Another problem is connected to the fact that while the continuum gauge field action is scale invariant , the lattice regularisation breaks this in-variance and the action of lattice instantons typically depends on their size. This might distort the size distribution of instantons and in particular can lead to an overproduction of small in-* Talk presented by T.G. Kovács † Research supported by DOE grant DE–FG02–92ER– 40672 stantons which can even spoil the scaling of the topological susceptibility. The framework of classically perfect fixed point (FP) actions [2] is particularly suitable to address these problems. Fixed point actions can be shown to have scale invariant instanton solutions and there are no charge 1 objects with an action lower than the continuum instanton action. The FP context also gives a consistent way of interpolation to define the topological charge. The fixed point action for any given configuration V on a lattice with lattice spacing a is defined by the weak coupling saddle-point equation where T is the blocking …