Three-fold Way at High Density

Abstract

The analysis of the Dirac spectrum in the last chapter for dense two-color QCD (corresponding to Dyson index \({\ss }=1\)) is extended to QCD with complex quarks at large isospin density (\({\ss }=2\)) and QCD with real quarks at large quark density (\(\beta =4\)), with “complex” and “real” referring to the representation of quarks under the gauge transformation. Namely two non-Hermitian chiral random matrix theories (ChRMT) are successfully identified that reduce, in the large-N limit, to those dense QCD-like theories with \({\ss }=2\) and 4 in the \(\varepsilon \)-regime. This establishes the generalization of the "three-fold way" (\({\ss }=1, 2, 4\)) of ChRMT a la Verbaarschot in the QCD vacuum to the BCS superfluid phase of dense QCD. The microscopic spectral density of random matrix eigenvalues in the new ChRMT is precisely determined, and its properties in comparison with two-color QCD are discussed.