The pressure and a possible hidden Hagedorn transition at large-N

TL;DR

This paper investigates the nonperturbative thermodynamics of pure gauge theories at large N, examining pressure deficits and searching for a Hagedorn transition, revealing similarities across different SU(N) groups and estimating the Hagedorn temperature.

Contribution

It provides numerical evidence of pressure deficits in SU(N) gauge theories and estimates the Hagedorn temperature in large N theories, extending understanding of nonperturbative QCD phenomena.

Findings

Pressure deficits are similar across SU(3), SU(4), and SU(8).

Estimated T_H/Tc for SU(12) is approximately 1.116.

The Hagedorn temperature exceeds the deconfinement temperature.

Abstract

In the first part of this contribution we present a numerical study motivated by recent attempts to understand the nonperturbative aspects of QCD at temperatures T~ a few times the deconfinement temperature Tc. We focus on the pure gauge theory, and ask whether the deficit in pressure and entropy, with respect to their free-gas values, is particular to SU(3). We find that the deficit in SU(4),SU(8) for T>= 2Tc,1.6 Tc, respectively, is remarkably close to that of SU(3). This suggests a similar deficit for SU(oo), which is fortunate since this theory is simpler, and can serve to constrain the possible dynamics underlying the deficits. In the second part we seek for signs of a Hagedorn temperature T_H in pure lattice SU(N) gauge theories with N=8,10,12. Since one expects T_H>Tc, we measure masses of strings in the metastable confined phase above Tc, and extrapolatethem to zero to estimate T_H. For SU(12) we find that T_H/Tc=1.116(9), when we extrapolate with a critical exponentof the three dimensional XY model, which seems to be preferred over a mean field exponent by our data.