QCD and the Hagedorn spectrum

TL;DR

This paper demonstrates that large Nc QCD necessarily exhibits a Hagedorn spectrum, with an exponential growth in the number of hadrons as their mass increases, under specific technical assumptions.

Contribution

It establishes a theoretical link between confinement, asymptotic freedom, and the Hagedorn spectrum in large Nc QCD, under certain assumptions.

Findings

Large Nc QCD has a Hagedorn spectrum if technical assumptions hold.

The spectrum growth is exponential with hadron mass.

The argument relies on confinement and asymptotic freedom interplay.

Abstract

It is shown that large Nc QCD must have a Hagedorn spectrum (i.e. a spectrum of hadron which grows exponentially with the hadrons mass) provided that certain technical assumptions concerning the applicability of perturbation theory to a certain class of correlation functions apply. The basic argument exploits the interplay of confinement and asymptotic freedom.