On finite-density QCD at large Nc

Deryagin, Grigoriev, and Rubakov (DGR) have shown that in finite-density QCD at infinite Nc the Fermi surface is unstable with respect to the formation of chiral waves with wavenumber twice the Fermi momentum, while the BCS instability is suppressed. We show here that at large, but finite Nc, the DGR instability only occurs in a finite window of chemical potentials from above ΛQCD to μcrit∼exp(γln2Nc+O(lnNcln lnNc))ΛQCD, where γ∼0.02173. Our analysis shows that, at least in the perturbative regime, the instability occurs only at extremely large Nc, Nc > or approx. 1000Nf, where Nf is the number of flavors. We conclude that the DGR instability is not likely to occur in QCD with three colors, where the ground state at finite density is expected to be a color superconductor. We speculate on the possible structure of the ground state of finite-density QCD with very large Nc