Chiral random matrix theory for colorful quark-antiquark condensates

Abstract

In QCD at high density, the color-octet quark-antiquark condensate $⟨\overline{\psi }{\gamma }_0({\lambda }^A{)}_C({\lambda }^A{)}_F\psi ⟩$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3{)}_C\times \mathrm{SU}(3{)}_L\times \mathrm{SU}(3{)}_R$ symmetry down to the diagonal $\mathrm{SU}(3{)}_V$. We evaluate this condensate in the mean-field approximation and find that it is of order $\mu {\Delta }^2\log (\mu /\Delta )$ where $\Delta$ 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.

Comments: 9 pages, 1 figure