Non-Abelian Debye screening length beyond leading order

In quantum electrodynamics, static electric fields are screened at nonzero temperatures by charges in the plasma. The inverse screening length, or Debye mass, may be analyzed in perturbation theory and is of order eT at relativistic temperatures. An analogous situation occurs when non-Abelian gauge theories are studied perturbatively, but the perturbative analysis breaks down when corrections of order ${\mathit{e}}^2$T are considered. At this order, the Debye mass depends on the nonperturbative physics of confinement, and a perturbative ‘‘definition’’ of the Debye mass as the pole of a gluon propagator does not even make sense. In this work, we show how the Debye mass can be defined nonperturbatively in a manifestly gauge-invariant manner (in vectorlike gauge theories with zero chemical potential). In addition, we show how the O(${\mathit{e}}^2$T) correction could be determined by a fairly simple, three-dimensional, numerical lattice calculation of the perimeter-law behavior of large, adjoint-charge Wilson loops. © 1995 The American Physical Society.