QCD and the Hagedorn spectrum

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.

Comments: 16 pages, 1 figure. This version is expanded from the original version. Additional discussion has been added to clarify the central issues. Typos have been fixed. The appendix has been updated and greatly expanded.