# Covariant variational approach to Yang-Mills Theory: Thermodynamics

## TL;DR

This paper investigates the thermodynamics of SU(2) Yang-Mills theory using a covariant variational approach, analyzing the pressure and related quantities across temperature regimes and comparing with lattice data.

## Contribution

It introduces a covariant variational framework for Yang-Mills thermodynamics, including analytic expressions and remedies for artifacts at low temperatures.

## Key findings

- Correct Stefan-Boltzmann limit at high T
- Artifacts at T→0 due to massless modes
- Good agreement with lattice data for pressure and energy density

## Abstract

The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational approach is studied by relating the free action density in the background of a non-trivial Polyakov loop to the pressure of the gluon plasma. The correct subtraction of the vacuum contribution in the free action density is argued for. The Poisson resummed expression for the pressure can be evaluated analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at $T \to \infty$, while the limit $T \to 0$ is afflicted by artifacts due to massless modes in the confined phase. Several remedies to remove these artifacts are discussed. Using the numerical $T=0$ solutions for the ghost and gluon propagators in the covariant variational approach as input, the pressure, energy density and interaction strength are calculated and compared to lattice data.