Abstract
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the infrared behavior of the gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge theory. We find that a very significant correlation of the real part of the Polyakov loop with the asymmetry as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We obtain the screening masses in different Polyakov-loop sectors and discuss the dependence of chromoelectric and chromomagnetic interactions of static color charges and currents on the choice of the Polyakov-loop sector in the deconfinement phase.
Highlights
It is widely hoped that the behavior of the Green’s functions of gauge fields encodes the confinement mechanism [1,2,3]
We have studied the asymmetry A and the longitudinal gluon propagator in the Landau-gauge SUð3Þ gluodynamics on lattices 243 × 8 over the range of temperatures 0.9Tc < T < 1.1Tc
The conditional averages hAiP1⁄4z or hDLð0ÞiP1⁄4z give a close approximation to the infinite-volume limit of A or DLð0Þ at the temperature τ determined from the equation P∞ðτÞ 1⁄4 z provided that z is an allowed infinite-volume value of the Polyakov loop in a chosen sector and P∞ is the infinite-volume expectation value of P
Summary
It is widely hoped that the behavior of the Green’s functions of gauge fields encodes the confinement mechanism [1,2,3]. Significant correlations between the chromoelectric-chromomagnetic asymmetry and the Polyakov loop as well as between the zero-momentum longitudinal propagator and the Polyakov loop were found in SU(2) gluodynamics [8,9]. This made it possible to describe critical behavior of the asymmetry and the propagator and to reliably evaluate finite-volume effects. We obtain the critical behavior of only the longitudinal propagator because it correlates with the real part of the Polyakov loop much more significantly than the transverse propagator Therewith, we evaluate both chromoelectric and chromomagnetic screening masses in all Polyakov-loop sectors and obtain their dependence on the temperature.
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