Topological Structure of the SU(3) Vacuum

Abstract

We investigate the topological structure of the vacuum in SU(3) lattice gauge theory. We use under-relaxed cooling to remove the high-frequency fluctuations and a variety of "filters" to identify the topological charges in the resulting smoothened field configurations. We find a densely packed vacuum with an average instanton size, in the continuum limit, of about 0.5 fm. The density at large sizes decreases as a large inverse power of the size. At small sizes we see some sign of a trend towards the asymptotic perturbative behaviour. We find that an interesting polarisation phenomenon occurs: the large topological charges tend to have, on the average, the same sign and are over-screened by the smaller charges which tend to have, again on the average, the opposite sign to the larger instantons. We also calculate the topological susceptibility for which we obtain a continuum value of about 187 MeV. We perform the calculations for various volumes, lattice spacings and numbers of cooling sweeps, so as to obtain some control over the associated systematic errors. The coupling range is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to 32x32x32x64.