and thus gauge fixing is needed to define them properly. Here, we follow [@Philipsen:2002az] and fix to Coulomb gauge. In parts we also consider the so-called color averaged free energy defined through the manifestly gauge independent correlation function of two Polyakov loops, $$\begin{aligned}
e^{-F_{\bar q q}(r)/T+C}&=&\frac{1}{9}\langle {{\rm Tr}}W(\vec{x}) {{\rm Tr}}W^{\dagger}(0) \rangle \nonumber\\
&=&\langle L(\vec{x})L^\dagger(\vec{y})\rangle\; .
\label{fav}\end{aligned}$$

The constant $C$ appearing in (\[f1\]), (\[f8\]) and (\[fav\]) also includes divergent self-energy contributions which require renormalization. Following [@Kaczmarek:2002mc] the free energies have been normalized such that the color singlet free energy approaches the heavy quark potential (solid line) at the smallest distance available on the lattice, $F_1(r/a=1, T)=V(r)$. In Sec. \[renormalization\] we will explain the connection of this procedure to the the renormalized Polyakov loop and show the resulting renormalization constants in Table \[tab:ren\].

Some results for the color singlet, octet and averaged quark anti-quark free energies are shown in Fig. \[saos\] for one temperature below and one temperature above deconfinement, respectively. The free energies calculated in different color channels coincide at large distances and clearly show the effects from string breaking below and color screening above deconfinement. The octet free energies above $T_c$ are repulsive for all distances while below $T_c$ the 