The Hagedorn spectrum and large $N_c$ QCD in 2+1 and 3+1 dimensions

TL;DR

This paper demonstrates that a Hagedorn spectrum, characterized by exponential growth in the number of hadrons with mass, naturally arises in large N_c QCD in 2+1 and 3+1 dimensions using correlation functions and perturbation theory.

Contribution

It provides a theoretical proof that a Hagedorn spectrum emerges in large N_c QCD in lower and higher dimensions based on correlation function analysis and perturbative assumptions.

Findings

Hagedorn spectrum appears in 2+1 and 3+1 dimensional large N_c QCD.

Correlation functions' short-time behavior supports exponential spectrum growth.

The proof relies on perturbation theory accurately describing correlation function traces.

Abstract

We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space correlation functions for composite operators constructed from quark and gluon fields and exploits the fact that the short time behavior of the correlators is known in QCD. The demonstration relies on one critical assumption: that perturbation theory accurately describes the trace of the logarithm of a matrix of point-to-point correlation functions in the regime where the perturbative corrections to the asymptotically free value are small.