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