  We discuss the phase structure of QCD_4 as a perturbative deformation of the
Topological Quantum Field Theory (TQFT). When we choose a special Maximal
Abelian gauge (MAG) as the gauge fixing, the TQFT sector is equivalent to a 2D
O(3) non-linear sigma model (NLSM). We consider the finite temperature case,
and investigate the effect of the boundary conditions and the phase structure
of the TQFT sector. It can have a deconfining phase under the twisted boundary
conditions. However, this phase is screened once pertubative parts are added.
We conclude that the information about the phase structure is encoded in the
U(1) background in the case of the MAG.
