Hadronic Density of States from String Theory

TL;DR

This paper calculates the hadronic density of states in certain confining gauge theories using string theory, revealing a Hagedorn density and proposing a semiclassical approximation for finite temperature behavior.

Contribution

It provides an exact finite temperature partition function for hadrons in a specific string theory limit and introduces a semiclassical approach to estimate the density of states in confining gauge theories.

Findings

The theory exhibits a Hagedorn density of states.

The semiclassical approximation captures the hadronic energy density of states.

The coefficient of the Hagedorn density relates to the gauge theory string tension.

Abstract

Exactly soluble string theories describing a particular hadronic sector of certain confining gauge theories have been obtained recently as Penrose-Gueven limits of the dual supergravity backgrounds. The effect of taking the Penrose-Gueven limit on the gravity side translates, in the gauge theory side, into an effective truncation to hadrons of large U(1) charge (annulons). We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Gueven limit of the Maldacena-Nunez embedding of N=1 SYM into string theory. It is established that the theory exhibits a Hagedorn density of states. Motivated by this exact calculation we propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.