Topological fluctuations in SU(2) gauge theory with staggered fermions: An explotary study

Abstract

We investigate some basic aspects of topological fluctuations in lattice QCD, in the version with two colours and four light flavours; and we do so in both the confining, chiral symmetry broken phase and in the non-confining, chirally symmetric phase. This latter phase is found to ccut not only high temperatures, just as in the pure gauge system, but also in small spatial volumes, which is unlike the pure gauge case. We derive the way the topological susceptibility should vary with quark mass at small quark masses. We find that the calculated topological susceptibility decerases to zero with the quark mass, with the theretically expected powers except — in the symmetric phase — at the very smallest values of the quark mass. We demonstrate that this anomalous behaviour can be understood as arising from the fact that the lattice topological “zero modes” are in fact sufficiently far from being zero. We also show, in the chirally symmetric phase, that, just as expected, the average distance between instantons and anti-instantons decreases with decreasing quark mass. We finish with a new and more precise estimate of the location of the finite-temperature transition in SU(2) with four light flavours.