Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories

TL;DR

This paper uses high-precision lattice calculations to show that the thermodynamics of SU(2) and SU(3) Yang-Mills theories in the confining phase can be accurately modeled by a gas of massive glueballs with an exponentially growing Hagedorn spectrum, derived from an effective string model.

Contribution

It provides a parameter-free theoretical prediction based on an effective bosonic string model that matches lattice results for SU(2) and SU(3) Yang-Mills theories.

Findings

Glueball gas model describes SU(2) thermodynamics well.

Hagedorn spectrum derived from string model matches lattice data.

Effective model accurately predicts SU(3) results from previous studies.

Abstract

We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Bors\'anyi et al. in JHEP 07 (2012) 056.