Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase

TL;DR

This paper develops a strong coupling expansion for finite temperature Yang-Mills theory, confirming the hadron resonance gas model in the confined phase and providing insights into thermodynamic properties and phase transition estimates.

Contribution

It introduces a formalism for strong coupling expansions at finite temperature and computes key thermodynamic quantities for SU(2), linking lattice results with hadron resonance models.

Findings

Free energy matches ideal glueball gas at next-to-leading order.

Screening masses are nearly temperature independent in the confined phase.

The series provides a basis for estimating phase transition couplings.

Abstract

We perform euclidean strong coupling expansions for Yang Mills theory on the lattice at finite temperature. After setting up the formalism for general SU(N), we compute the first few terms of the series for the free energy density and the lowest screening mass in the case of SU(2). To next-to-leading order the free energy series agrees with that of an ideal gas of glueballs. This demonstrates that in the confined phase the quasi-particles indeed correspond to the T=0 hadron excitations, as commonly assumed in hadron resonance gas models. Our result also fixes the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method. In accord with Monte Carlo results, we find screening masses to be nearly temperature independent in the confined phase. This and the exponential smallness of the pressure can be understood as genuine strong coupling effects. Finally, we analyse Pade approximants to estimate the critical couplings of the phase transition, which for our short series are only ~25% accurate. However, up to these couplings the equation of state agrees quantitatively with numerical results on N_t=1-4 lattices.