Quarkyonic Meson Matter for Finite Isospin Density

QCD at finite isospin density is considered for a large number of colors $N_c$. A linear sigma model is used to model the meson content of the theory at low density. At isospin chemical potential $\mu_I << \Lambda_{QCD}$, this matter forms a Bose condensate. For $\mu_I >> \sqrt{N_c} \Lambda_{QCD}$, unlike QCD remains confined, but the degrees of freedom of the system are mesons and Cooper pairs bound on size scales small compared to the QCD size scale determined by the superfluid gap. For most purposes this matter may be analyzed using weak coupling methods. For $\Lambda_{QCD} \le \mu_I \le \sqrt{Nc} \Lambda_{QCD}$, we argue that meson matter is quarkyonic, with quarks bound into mesons on a size scale of order $\Lambda_{QCD}$ corresponding to a filled Fermi sea of quarks, with possible Bose condensation at the Fermi surface and/or Cooper pairs with finite width of the surface of order $\Lambda_{QCD}$.