Dense QCD in a Finite Volume

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.

4 pages, 1 figure; v3. changed figure, added comments and references, final version to appear in Phys. Rev. Lett

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Cited by in corpus (27)

• Vortices and Other Topological Solitons in Dense Quark Matter
• Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions
• The NJL model of dense three-flavor matter with axial anomaly: the low temperature critical point and BEC-BCS diquark crossover
• Universality of Phases in QCD and QCD-like Theories
• Singular values of the Dirac operator in dense QCD-like theories
• Finite-size scaling as a tool in the search for the QCD critical point in heavy ion data
• Chiral random matrix theory for two-color QCD at high density
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• U(1) axial symmetry and Dirac spectra in QCD at high temperature
• The Myriad Uses of Instantons
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Chiral symmetry breaking with no bilinear condensate revisited
• Magnetic Tuning of the Relativistic BCS-BEC Crossover
• Banks-Casher-type relation for the BCS gap at high density
• Nambu-Jona-Lasinio model in a sphere
• SU(3) deconfining phase transition with finite volume corrections due to a confined exterior
• Handbook Article on Applications of Random Matrix Theory to QCD
• Equation of State in a Strongly Interacting Relativistic System
• BCS-BEC Crossover and Stability in a Nambu-Jona-Lasinio Model with Diquark-Diquark Repulsion
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Heavy-tailed chiral random matrix theory
• Relativistic Cooper pairing in the microscopic limit of chiral random matrix theory
• Random matrix model for chiral and color-flavor locking condensates
• Chiral Lagrangian and spectral sum rules for two-color QCD at high density
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Singular values of the Dirac operator at nonzero density