Topological Structure of the SU ( 3 ) Vacuum UKQCD Collaboration

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 ρ̄ ∼ 0.5 fm. The density at large ρ decreases rapidly as 1/ρ. At small sizes we see some signs of a trend towards the asymptotic perturbative behaviour of D(ρ) ∝ ρ. 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, χt, for which we obtain a continuum value of χ 1/4 t ∼ 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 6.0 ≤ β ≤ 6.4 and the lattice volumes range from 1648 to 3264.