Asymptotic behavior of the correlator for Polyakov loops.

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. One of the basic characteristics of a plasma is the screening of electric fields. The field created by a static charge falls off exponentially beyond the screening radius, whose inverse is called the Debye mass mD. In a quark-gluon plasma at high temperature T , chromoelectric fields are believed to be screened in a similar way. However it has proven to be difficult to give a precise definition to the Debye mass in perturbation theory. At leading order in the coupling constant g, mD is proportional to gT . The next-to-leading order correction to mD has been calculated using a resummed perturbation theory in which gluon propagator corrections of order gT 2 are summed up to all orders [1, 2]. The correction is gauge-invariant but infrared-divergent, indicating a sensitivity to nonperturbative effects involving the scale gT . Debye screening can also be studied nonperturbatively using lattice simulations [3, 4, 5]. One of the simplest probes of Debye screening is the correlator of two Polyakov loop operators as a function of their separation R. At lowest order in resummed perturbation theory, the behavior of the correlator is predicted to be exp(−2mDR)/R. By fitting the measured correlator to this form, one can extract a value for mD. However the resummed perturbation expansion is known to break down at higher orders, due to contributions that involve the exchange of magnetostatic gluons. These contributions, which are inherently nonperturbative, can be expected to dominate at distances R much greater than 1/mD. This raises questions about the utility of determining mD by fitting the correlator to a leading order expression. In this paper, we determine the true asymptotic behavior of the Polyakov loop correlator at large R. We use effective field theory methods to express the Polyakov loop operator in terms of operators in 3-dimensional QCD. The asymptotic behavior of the Polyakov loop correlator is then given by a simple correlator in this effective theory. It has the form exp(−mHR)/R, where mH is the mass of the lowest glueball state in (2+1)-dimensional QCD. The coefficient of the exponential is of order g. Our result implies that the asymptotic behavior of the Polyakov loop correlator is dominated by magnetostatic effects which have little to do with Debye screening. We wish to study the correlator of Polyakov loop operators in thermal QCD in 4 spacetime dimensions with temperature T . The fundamental fields are the gauge field Aμ(x, τ),