Hagedorn spectrum and equation of state of Yang-Mills theories

TL;DR

This paper introduces a lattice-based approach to compute the equation of state for SU(2) Yang-Mills theory, showing that a glueball gas with a Hagedorn spectrum accurately models the confining phase.

Contribution

It demonstrates that a bosonic string-inspired Hagedorn spectrum effectively describes the glueball spectrum and thermodynamics in SU(2) Yang-Mills theory, extending to SU(3) with good agreement.

Findings

Glueball gas models match lattice data well

Hagedorn spectrum derived from string models explains heavy glueball states

The approach predicts the equation of state accurately in the confining phase

Abstract

We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\'anyi et al. in JHEP 07 (2012) 056.