Chiral random matrix theory for colorful quark-antiquark condensates

Abstract

In QCD at high density, the color-octet quark-antiquark condensate ψγ0(λ A )C (λ A )F ψ is generally nonzero and dynamically breaks the SU(3)C ×SU(3)L ×SU(3)R symmetry down to the diagonal SU(3)V . We evaluate this condensate in the mean-field approximation and find that it is of order µ∆ 2 log(µ/∆) where ∆ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-N limit and find that three phases appear depending on the parameter of the model. They are the color-flavor locked phase, the polar phase, and the normal phase. We rigorously derive the effective theory of Nambu-Goldstone modes and determine the quark-mass dependence of the partition function.