$T\;\gsim\;T_c$ and intermediate distances and demonstrates the difficulty to separate clearly the different effects usually described by color screening and string breaking in the vicinity of the phase transition. We note here, however, that similar to the coupling in quenched QCD [@Kaczmarek:2004gv] the coupling which describes the short distance Coulombic part in the free energies is almost temperature independent in this temperature regime, [*i.e.*]{} even at relatively large distances the free energies shown in Fig. \[fes\] show no or only little temperature dependence below deconfinement.

Renormalization of the quark anti-quark free energies and Polyakov loop {#renormalization}
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On the lattice the expectation value of the Polyakov loop and its correlation functions suffer from linear divergences. This leads to vanishing expectation values in the continuum limit, $a\to0$, at all temperatures. To become a meaningful physical observable a proper renormalization is required [@Kaczmarek:2002mc; @Dumitru:2004gd; @deForcrand:2001nd]. We follow here the conceptual approach suggested in [@Kaczmarek:2002mc; @Phd] and extend our earlier studies in pure gauge theory to the present case of 2-flavor QCD. First experiences with this renormalization method in full QCD were already reported in [@Kaczmarek:2003ph; @Petreczky:2004pz].

In the limit of short distances, $r\ll1/T$, thermal modifications of the quark anti-quark free energy become 