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

## TL;DR

This paper uses a variational approach with the Gaussian Effective Potential to demonstrate mass generation and deconfinement in pure Yang-Mills theory, predicting a phase transition at around 255 MeV consistent with lattice data.

## Contribution

It introduces a variational GEP method to analyze mass generation and phase transition in Yang-Mills theory, providing new insights into the deconfinement process.

## Key findings

- Massive gaussian vacuum is more stable than massless vacuum.
- Predicts a weakly first-order phase transition at T_c ≈ 255 MeV.
- Equation of state matches lattice results.

## Abstract

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.