Yang-Mills effective action at high temperature

Yang-Mills theory undergoes a transition from a confined to a deconfined phase in the intermediate temperature regime, where perturbation is not applicable. In order to approach this phase transition from the high temperature side we study the effective action for the eigenvalues of the order parameter, the Polyakov loop. By means of a covariant derivative expansion we integrate out fast varying quantum fluctuations around background gluon fields and assume that these are slowly varying, but that the amplitude of A(4) is arbitrary. Our results can be used to study correlation functions of the order parameter at high temperatures.