QCD Instantons in Vacuum and Matter

Abstract

The singlet coupling to the topological charge density in the instanton vacuum, causes the instantons and antiinstantons to be screened over distances of the order of 1/2 fm. Dilute instanton systems behave as a free gas, while dense instanton systems behave as a plasma. The free gas behaviour is favored by a density of 1 fm$^{-4}$. Owing to the Higgs mechanism, the $η$' mass is heavy (1100 MeV). The vacuum topological susceptibility is small (0.07 fm$^{-4}$) and consistent with the QCD Ward identity. In the chiral limit, the singlet screening vanishes, leading to a four dimensional plasma state with a temperature given by the nonet decay constant $f$ (90 MeV). The phase is Debye screened. In the presence of matter, the screening is quenched, and a Kosterlitz-Thouless transition may occur signaling the restoration of the $U_A(1)$ symmetry. We suggest to use the spatial asymptotics of the static topological charge correlator together with the topological susceptibility to probe the interplay between the $U_A(1)$ restoration and the chiral restoration in finite temperature QCD. The relevance of these results to the bulk thermodynamics in the instanton vacuum is discussed.