Relativistic Cooper pairing in the microscopic limit of chiral random matrix theory
arXiv:2004.04483 · doi:10.1142/S0217732326500872
Abstract
Random matrix theory (RMT) provides a powerful framework for analyzing universal features of strongly coupled physical systems. In quantum chromodynamics (QCD), cold quark matter at asymptotically high density is expected to exhibit color superconductivity (CSC), the analogue of superconductivity in condensed-matter systems. Although CSC phases have been studied within RMT primarily in the macroscopic large- limit, where denotes the matrix size, it has remained unclear whether an RMT exists that realizes CSC in the microscopic large- limit. Here we answer this question in the affirmative by introducing a novel non-Hermitian chiral random matrix model. For three quark flavors, we show that the model exhibits spontaneous breaking of color and flavor symmetries down to the diagonal subgroup, thereby reproducing color-flavor locking in dense QCD. For two flavors, we find that color is spontaneously broken to while the chiral symmetry remains unbroken, consistent with the two-flavor color-superconducting phase.
16 pages. v2: two-flavor analysis added in Section 4. v3: matches published version
References in corpus (42)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Color superconductivity in dense quark matter
- QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
- Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD
- The phase diagram of dense QCD
- Diquark Bose Condensates in High Density Matter and Instantons
- On the Phase Diagram of QCD
- Random matrix theory and spectral sum rules for the Dirac operator in QCD
- The Condensed Matter Physics of QCD
- Random Matrix Theory and Chiral Symmetry in QCD
- Random matrix model of QCD at finite density and the nature of the quenched limit
- Continuity of Quark and Hadron Matter
- QCD-like Theories at Finite Baryon Density
- Inverse meson mass ordering in color-flavor-locking phase of high density QCD
- Universal results from an alternate random matrix model for QCD with a baryon chemical potential
- From chiral Random Matrix Theory to chiral Perturbation Theory
- Inverse meson mass ordering in color-flavor-locking phase of high density QCD: erratum
- Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
- Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
- Instanton Effects in QCD at High Baryon Density
- Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
- Singular values of the Dirac operator in dense QCD-like theories
- Mass Terms in Effective Theories of High Density Quark Matter
- Matrix Models and QCD with Chemical Potential
- Universality near zero virtuality
- Chiral Lagrangian and spectral sum rules for dense two-color QCD
- Random matrix model for chiral symmetry breaking and color superconductivity in QCD at finite density
- Chiral random matrix theory for two-color QCD at high density
- Anyonic particle-vortex statistics and the nature of dense quark matter
- Dense QCD in a Finite Volume
- Universality of Correlation Functions in Random Matrix Models of QCD
- Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
- The chiral Gaussian two-matrix ensemble of real asymmetric matrices
- Quark description of the Nambu-Goldstone bosons in the color-flavor locked phase
- Banks-Casher-type relation for the BCS gap at high density
- Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
- Lecture Notes on Superconductivity: Condensed Matter and QCD
- Microscopic spectral density in random matrix models for chiral and diquark condensation
- Random matrix models for phase diagrams
- Chiral random matrix theory for single-flavor spin-one Cooper pairing
- Random matrix model for chiral and color-flavor locking condensates
- Chiral random matrix theory for colorful quark-antiquark condensates