Asymptotic Behavior of the Correlator for Polyakov Loops

The correlator for Polyakov loop operators in high temperature QCD is studied by using dimensionally reduced effective field theories. The Polyakov loop operator is expanded in terms of local gauge-invariant operators constructed out of the magnetostatic gauge field, with coefficients that can be calculated using resummed perturbation theory. The asymptotic behavior of the correlator is $\exp (-MR)/R$, where $M$ is the mass of the lowest-lying glueball in $(2+1)$-dimensional QCD. This result implies that existing lattice calculations of the Polyakov loop correlator at the highest temperatures available do not probe the true asymptotic region.