A Model for the Effective Potential of Thermalized Pure SU(Large N) Gauge Theory

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.