Superconductivity by long-range color magnetic interaction in high-density quark matter

We argue that in quark matter at high densities, the color magnetic field remains unscreened and leads to the phenomenon of color superconductivity. Using the renormalization group near the Fermi surface, we find that the long-range nature of the magnetic interaction changes the asymptotic behavior of the gap $\Delta$ at large chemical potential $\mu$ qualitatively. We find $\Delta \sim \mu g^{-5}\exp \left[\right(-3{\pi }^2/\sqrt{2})/g]$, where g is the small gauge coupling. We discuss the possibility of breaking rotational symmetry by the formation of a condensate with nonzero angular momentum, as well as interesting parallels to some condensed matter systems with long-range forces.