Chiral random matrix theory for single-flavor spin-one Cooper pairing

Abstract

We propose a new non-Hermitian chiral random matrix model that describes single-flavor spin-one Cooper pairing of quarks. For three colors the model shows spontaneous breaking of color $\mathrm{SU}(3{)}_C$ and spin $\mathrm{SO}(3{)}_J$ symmetries down to the diagonal $\mathrm{SO}(3{)}_{C+J}$ subgroup, in striking analogy to the color-spin locked phase of one-flavor QCD at high density. For two colors, color-singlet spin-one diquarks condense and trigger symmetry breaking $\mathrm{U}(1)\times \mathrm{SO}(3{)}_J\to \mathrm{SO}(2{)}_J$. In both cases the microscopic large-$N$ limit is rigorously taken and the effective theory of Nambu-Goldstone modes is derived.

Comments: 9 pages