Statistical QCD with non-positive measure

TL;DR

This paper explores the microscopic behavior of QCD at nonzero chemical potential, revealing how complex oscillations in the spectral density of the Dirac operator cause the chiral condensate to exhibit a discontinuity at zero quark mass, using random matrix models.

Contribution

It establishes an exact relation between spectral oscillations and the chiral condensate discontinuity in QCD at nonzero chemical potential, advancing understanding of the sign problem.

Findings

Spectral density exhibits violent complex oscillations.

Oscillations cause the chiral condensate discontinuity.

Random matrix models accurately describe the phenomena.

Abstract

In this talk we discuss the microscopic limit of QCD at nonzero chemical potential. In this domain, where the QCD partition function is under complete analytical control, we uncover an entirely new link between the spectral density of the Dirac operator and the chiral condensate: violent complex oscillations on the microscopic scale give rise to the discontinuity of the chiral condensate at zero quark mass. We first establish this relation exactly within a random matrix framework and then analyze the importance of the individual modes by Fourier analysis.