Baryon Number Dirac Spectrum in QCD

TL;DR

This paper investigates how extreme oscillations in the spectral density of the baryon number Dirac operator, caused by the QCD sign problem, are crucial for understanding the average baryon number at nonzero chemical potential.

Contribution

It demonstrates the role of spectral density oscillations in baryon number formation and employs chiral perturbation theory and random matrix theory to analyze these phenomena.

Findings

Spectral density oscillations are essential for baryon number formation.

Extreme oscillations have a microscopic period.

Random matrix theory resolves the oscillations.

Abstract

The relation between the baryon number in QCD at nonzero chemical potential and the spectral density of the baryon number Dirac operator, $\gamma_0(D+m)$, is examined. We show that extreme oscillations of the spectral density, caused by the QCD sign problem, are essential for the formation of the average baryon number when $\mu>m_\pi/2$. We compute the oscillating region of the spectral density using chiral perturbation theory. The extreme oscillations have a microscopic period and are resolved using random matrix theory.