Mass generation and deconfinement in pure Yang-Mills theory: a variational study

A simple variational argument based on the Gaussian Effective Potential (GEP) is put forward to give evidence for mass generation and deconfinement in pure Yang-Mills SU(N) theory. The GEP analysis shows that the massless gaussian vacuum of Yang-Mills theory is perturbatively unstable towards a massive gaussian vacuum, indicating that a massive expansion is the natural choice for computations in YMT. At finite temperature, the GEP provides an optimal temperature-dependent mass parameter for the expansion and signals the occurrence of a weakly first-order phase transition at $T_{c}\approx$ 255 MeV for $N=3$. The equation of state is found to be in good agreement with the lattice data. This work is complemented with review material on the standard and massive expansions of Yang-Mills theory and on the formalism of quantum field theory at finite temperature. Comparisons are made with lattice results and numerical tables are provided to support our findings.