Aspects of high density QCD

Abstract

The recent study on high density QCD under zero temperature within recent one or two years is reviewed. It is known from the works of D. Balin and A. Love, who assume that the magnetic gluons are screened, that the high density QCD represents the color superconductor and the magnitude of the gap is order of $e^{-const}/g^2}$, equal to usual BCS superconducting gap in the exponential behavior. However, the recent analysis, which include long-range color magnetic interaction, in two alternative ways, based on the gap equation and renormalization group analysis, shows that the gap is order of $e^{-const}/g$. Then the latter is much larger than the former in the high density limit, where g is very small. In this review, using effective field theory near the Fermi surface, we will obtain the marginal four-quark interaction describing the scattering of two quarks with equal and opposite momenta as we approach to the Fermi surface and then we will see that this four-quark interaction generates the color diquark condensate through the gap equation. Also in the sense of Wilsonian renormalizaton group we obtain the RG equation for the scattering amplitude given by the above four-quark interaction. The solution of this RG equation has a singularity, which is the manifestation of BCS instability, in the color anti-triplet, s-wave channel. This singularity called "Landau pole" gives the gap of order $e^{-const}/g$ when the long-range color magnetic interacton is considered. Although it is known that the only color anti-triplet channel is attractive, for the three massless flavor case the general requirement of the Fermi statistics, which requires the gap matrix is symmetric in simultaneous exchange of both color and flavor indices, and the special operator makes it possible to have condensate in the repulsive channel. Thus in high density what is found is the mixture of condensate in attractive and repulsive channel called "color-flavor-locked"(CFL) condensate. This CFL con...