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Abstract: We study the properties of QCD at high baryon density in a finite volumewhere color superconductivity occurs. We derive exact sum rules for complexeigenvalues of the Dirac operator at finite chemical potential, and show thatthe 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 massplane near the origin, reflecting the $Z2 {L} \times Z2 {R}$ symmetry ofthe 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 $m {\pi}$ isthe pion mass at high density.

Autor: Naoki Yamamoto, Takuya Kanazawa


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