Polyakov Loops versus Hadronic States

The order parameter for the pure Yang-Mills phase transition is the Polyakov loop which encodes the symmetries of the Z_N center of the SU(N) gauge group. On the other side the physical degrees of freedom of any asymptotically free gauge theory are hadronic states. Using the Yang-Mills trace anomaly and the exact Z_N symmetry we construct a model able to communicate to the hadrons the information carried by the order parameter.