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

TL;DR

This paper introduces a simple variational method using the Gaussian effective potential to study mass generation and deconfinement in pure SU(N) Yang-Mills theory, providing analytical insights and matching lattice results.

Contribution

It presents a novel variational approach based on the Gaussian effective potential in a covariant gauge for Yang-Mills theory, enabling analytical study of mass generation and phase transition.

Findings

Identifies a weak first-order deconfinement transition at T_c≈250 MeV for N=3.

Shows the mass scale drops discontinuously at the transition.

Finds the equation of state agrees well with lattice data.

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.