Topological structure of the SU(3) vacuum

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 $\overline{\rho }\sim 0.5\mathrm{fm}.$ The density at large ρ decreases rapidly as $1/{\rho }^{\sim 11}.$ At small sizes we see some signs of a trend towards the asymptotic perturbative behavior of $D\left(\rho \right)\propto {\rho }^6.$ We find that an interesting polarization 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, ${\chi }_t,$ for which we obtain a continuum value of ${\chi }_t^{1/4}\sim 187\mathrm{MeV}.$ 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 $6.0<~\beta <~6.4$ and the lattice volumes range from ${16}^3\times 48$ to ${32}^3\times 64.$