Variational study of mass generation and deconfinement in Yang-Mills theory

Abstract

A very simple variational approach to pure SU($N$) Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at $T_c\approx 250$ MeV for $N=3$) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.

Comments: Final published version. Important material added in the new versions: improved variational ansatz (yielding better agreement with the lattice); new details on the status of the dynamical mass in Section III on regularization and renormalization; a new discussion on Jensen inequality in Section V; details on the limits $T\to 0$ and $\alpha \to 0$