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

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 Borsányi et al. in JHEP 07 (2012) 056.

Comments: 1+19 pages, 4 pdf figures; v2: 1+22 pages, 4 pdf figures, improved discussion in sections 3 and 4, added references, corrected misprints: matches the journal version; v3: corrected a misprint, pointed out to us by Etsuko Itou, in the discussion of eq. (3.1), results unaffected