  Based on the (in part verified) ideas of a dynamical ``abelian-ization'' and
subsequent ``center-ization'' of pure SU($N$) gauge theory an effective
potential for relevant field variables is constructed in the limit of large N.
To do this the theory is assumed to be thermalized and to be gravitationally
deformed. BPS saturation in the dynamics of the monopole field is shown to lead
to a suppression of the back reaction due to classical gravity. The classical,
effective description of the gauge theory can be justified for both the regime
of maximal abelian gauge symmetry and the center symmetric phase.
