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.
Categories: hep-th cond-mat.supr-con hep-lat hep-ph