A Random Matrix Model for Color Superconductivity at Zero Chemical Potential

TL;DR

This paper uses a random matrix model to analyze symmetry breaking in QCD at zero chemical potential, finding that chiral symmetry breaking dominates and stable diquark phases are unlikely.

Contribution

It introduces a random matrix framework to study symmetry breaking in QCD, revealing that diquark condensates are not thermodynamically favored at zero chemical potential.

Findings

Chiral symmetry breaking is thermodynamically preferred.

Stable diquark condensates only appear as rotated chiral condensates.

No independent diquark phase forms in two-flavor QCD at zero chemical potential.

Abstract

We discuss random matrix models for the spontaneous breaking of both chiral and color symmetries at zero chemical potential and finite temperature. Exploring different Lorentz and gauge symmetric color structures of the random matrix interactions, we find that spontaneous chiral symmetry breaking is always thermodynamically preferred over diquark condensation. Stable diquark condensates appear only as SU(2) rotated chiral condensates, which do not represent an independent thermodynamic phase. Our analysis is based on general symmetry arguments and hence suggests that no stable and independent diquark phase can form in QCD with two flavors at zero quark chemical potential.