Universal aspects in the equation of state for Yang-Mills theories

TL;DR

This paper demonstrates that the thermodynamics of various Yang-Mills theories can be universally described by a glueball gas model with an Hagedorn spectrum, matching lattice data across different gauge groups and phases.

Contribution

It introduces a universal glueball gas model with an Hagedorn spectrum that accurately describes the equation of state in both confining and deconfined phases of Yang-Mills theories.

Findings

Glueball gas model fits lattice data well in confining phase.

Equation of state in deconfined phase proportional to gluon degrees of freedom.

Model describes SU(3), SU(2), and G2 gauge theories accurately.

Abstract

We present high-precision lattice calculations of the thermodynamics of Yang-Mills theories with different gauge groups. In the confining phase, we show that the equation of state is described remarkably well by a gas of massive, non-interacting glueballs, provided that an effective bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy states. In particular, this model describes very accurately the results for the SU(3) theory reported by Bors\'anyi et al. in JHEP 07 (2012) 056, as well as a novel set of lattice data for the SU(2) theory. In addition, we also also show that the equation of state in the deconfined phase exhibits a near perfect proportionality to the number of gluon degrees of freedom, including for the Yang-Mills theory based on the exceptional, center-less gauge group $G_2$.