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 similar or equal to 1/5T(c), at which most other physical quantities show small lattice spacing corrections. Our T similar or equal to 0 topological susceptibility appears to approach a finite non-zero limit at N = infinity that is consistent with earlier extrapolations from smaller values of N. Near the deconfining temperature T-c, 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 -> infinity the large-T suppression of large instantons and the large-N suppression of small instantons overlap, even at T similar or equal to 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(p) infinity 8(p - p(c)) at N = infinity, with p(c) similar to 1/ T-c. (c) 2005 Elsevier B.V. All rights reserved.