Wilson line in finite-temperature gauge theories

The phases of SU(N) gauge theories at finite temperature can be analyzed in terms of the Wilson line $L({{→}}{x})=TrPexp[ig {∫}{0}^{{β}}{A}₀({{→}}{x},{τ})d{τ}]$. The question of confinement is related to the spontaneous breakdown of a $Z(N)$ symmetry: $〈L〉{≠}0$ corresponds to symmetry breaking and deconfinement, $〈L〉=0$ implies symmetry restoration and confinement. A previous calculation of the one-loop effective potential for $L$ is discussed in $SU(N)$ theories, both with and without fermions. A possible mechanism for the confining-deconfining transition in terms of the formation of "$Z(N)$ bubbles" is discussed. For SU(2) theories, the $Z(2)$ bubbles are simply finite-temperature instantons. However, $Z(N)$ bubbles are not finite-temperature instantons for $SU(N)$. It is shown that a bag picture of hadronic structure similar to that of Callan, Dashen, and Gross may emerge from this picture.