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

TL;DR

This paper investigates the topological properties of SU(N) gauge theories at zero and finite temperature, revealing that topological fluctuations are suppressed in the deconfined phase at large N, while remaining similar to zero-temperature behavior in the confined phase.

Contribution

It provides the first detailed analysis of topological charge density and susceptibility across different N and phases, showing suppression of fluctuations at large N in the deconfined phase.

Findings

Topological susceptibility approaches a finite non-zero limit as N→infinity at T=0.

In the deconfined phase at large N, topological fluctuations are suppressed, with rare instantons.

The size distribution of instantons becomes sharply peaked at N→infinity, near 1/Tc.

Abstract

We calculate the topological charge density of SU(N) lattice gauge fields for values of N up to N=8. Our T=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 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 of the confined phase is always very similar to that at T=0. By contrast, in the deconfined phase 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=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 D(rho) is proportional to a delta function at N=infinity, centered on rho close to 1/Tc.