Thermal Gauge Theory, Effective Action and Z(N) Symmetry

One of the salient features of high temperature gluodynamics is the Z(N) groundstate degeneracy, key to the understanding of the transition. On the other hand impressive progress has been obtained with effective theories, that seemingly lack Z(N) symmetry. We give a simple unified desciption of the two. As a very useful byproduct we get a natural infrared regulator and show its expediency by calculating the next to leading order in the Debye mass. Higher order corrections to bulk free energy and domainwall surface tension are discussed.