Topology of SU(N) gauge theories at T≃0 and T≃Tc

We calculate the topological charge density of SU(N) lattice gauge fields for values of N up to N=8. The calculations are performed mostly at a fixed lattice spacing, a≃1/5Tc, at which most other physical quantities show small lattice spacing corrections. Our T≃0 topological susceptibility appears to approach a finite non-zero limit at N=∞ that is consistent with earlier extrapolations from smaller values of N. Near the deconfining temperature Tc, we are able to investigate separately the confined and deconfined phases, since the transition is quite strongly first order. We find that the topological susceptibility in the confined phase is very similar at all T to that at T=0. By contrast, in the deconfined vacuum at larger N there are no topological fluctuations except for rare, isolated and small instantons. This shows that as N→∞ the large-T suppression of large instantons and the large-N suppression of small instantons overlap, even at T≃Tc, so as to suppress all topological fluctuations in the deconfined phase. In the confined phase by contrast, the size distribution is much the same at all T, becoming more peaked as N grows, suggesting that perhaps D(ρ)∝δ(ρ−ρc) at N=∞, with ρc∼1/Tc.