Dense QCD in a Finite Volume

Understand

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.