  The asymptotic behavior of the correlator for Polyakov loop operators
separated by a large distance $R$ is determined for high temperature QCD. It is
dominated by nonperturbative effects related to the exchange of magnetostatic
gluons. To analyze the asymptotic behavior, the problem is formulated in terms
of the effective field theory of QCD in 3 space dimensions. 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 in $R$.
