Deconfinement transition in SU(N) theories from perturbation theory

Understand

We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$) Yang-Mills theory.

• We compute the corresponding one-loop effective potential for a temporal background gluon field at finite temperature.
• At this order the background field is simply related to the Polyakov loop, the order parameter of the deconfinement transition.
• Our perturbative calculation correctly describes a quark confining phase at low temperature and a phase transition of second order for $N=2$ and weakly first order for $N=3$.