Dense QCD in a Finite Volume

TL;DR

This paper investigates the spectral properties of QCD at high baryon density in finite volumes, revealing a direct link between the Dirac spectrum and color superconductivity, with universal signatures in the eigenvalue distribution.

Contribution

It derives exact sum rules for the Dirac operator eigenvalues at finite chemical potential and identifies universal spectral signatures of color superconductivity in finite-volume QCD.

Findings

Dirac spectrum directly related to the superconducting gap Δ

Characteristic X-shaped spectrum of partition function zeros

Universal spectral signatures in the specified volume domain

Abstract

We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap $\Delta$. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the $Z(2)_{L} \times Z(2)_{R}$ symmetry of the diquark pairing. Our results are universal in the domain $\Delta^{-1} \ll L \ll m_{\pi}^{-1}$ where $L$ is the linear size of the system and $m_{\pi}$ is the pion mass at high density.