erature [@BGMP].

For the comparison we have computed the present flow with the zero-temperature running coupling in Fig. \[fig:alpha\] for all temperatures. This mimics the approximation used in [@Braun:2007bx], which implicitly relies on the zero-temperature running coupling $\alpha_s$. We also remark that the quantity $L[\langle A_0\rangle]$ in general is gauge-dependent, and only the critical temperature derived from it is not. However, in Landau-DeWitt gauge with backgrounds $A_0$ in Polyakov gauge temporal fluctuations about this background include those in Polyakov gauge. For this reason we might expect a rather quantitative agreement for the quantity $L[\langle A_0\rangle]$ in both approaches. The results for the temperature dependence of the Polyakov loop are depicted in Fig. \[fig:compare\].

![Comparison of $L[\langle A_0\rangle]$ computed in Polyakov gauge and in Landau-DeWitt gauge from [@Braun:2007bx].[]{data-label="fig:compare"}](LGcompare.eps "fig:"){width="8cm"}\

The coincidence between the two gauges is very remarkable, particularly since the mechanisms driving confinement are quite different in the different approaches, as are the approximations used in both cases. This provides further support for the respective results. It also sustains the argument concerning the lack of gauge dependence made above. The quantitative deviations in the vicinity of the phase transition are due to the truncation used in [@Braun:2007bx], that cannot encode the correct critical physics yet, as has been already discussed there.

Summary and outlook {#sec:summ}
===================

In the present work we have put forward a formulation of QCD in Polyakov gauge. We have argued that this gauge is specifically well-adapted for the investigation of the confinement-deconfinement phase transition as the order parameter, the Polyakov loop expectation value $\langle L[A_0]\rangle $, has a simple representation in terms of the temporal gauge field. Moreover, we have shown that $L[\langle
A_0\rangle]$ also serves as an orde