Dynamical role of Polyakov loops in the QCD thermodynamics
  Polyakov loops $L_a(T), a=3,8,...$ are shown to give the most important nonperturbative contribution to the thermodynamic potentials. Derived from the gluonic field correlators they enter as factors into free energy. It is shown in the $SU(3)$ case that $L_a (T)$ define to a large extent the behavior of the free energy and the trace anomaly $I(T)$, most sensitive to nonperturbative effects. 
N.O. Agasian, M.S. Lukashov, Yu.A. Simonov
hep-lat hep-ph hep-th