The goal of the high energy heavy-ion collision program at Relativistic Heavy Ion Collider in Brookhaven and the Large Hadron Collider at CERN is to study the theory of strong interactions, Quantum Chromodynamics, in extreme conditions. At very high temperatures achieved in the collisions, it is expected that quarks and gluons are deconfined to form the quark-gluon plasma.
In this talk, I will discuss this high temperature phase of QCD. To make the problem more tractable I will consider only gluon degrees of freedom and the limit of large number of colors. I will show that the effective potential is a simple function of the Polyakov loop. This will be explicitly demonstrated by perturbative two-loop calculations. I will report on our progress computing the three loop potential.