Strong coupling expansion for Yang-Mills theory at finite temperature

TL;DR

This paper applies strong coupling expansion to lattice Yang-Mills theory at finite temperature, providing insights into the confined phase, glueball gas behavior, and aiding Monte Carlo calculations near the deconfinement transition.

Contribution

It introduces a finite radius of convergence strong coupling expansion for Yang-Mills theory at finite temperature, connecting series results to physical phenomena like glueball gas and deconfinement.

Findings

Series sum corresponds to a glueball gas of lowest mass glueballs.

Lower integration constant for pressure is exponentially small in the confined phase.

Explains weak temperature dependence of glueball screening masses below T_c.

Abstract

Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for $\beta<\beta_c$, where $\beta_c$ denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the confined regime up to the deconfinement transition. We have calculated the first few orders of these expansions of the free energy density as well as the screening masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the weak temperature dependence of glueball screening masses below $T_c$, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting $\beta_c$ from the series are discussed.