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

TL;DR

The paper addresses color superconductivity in high-density quark matter where color magnetic interactions remain unscreened, causing infrared challenges for standard BCS analyses. It develops a renormalization-group framework around the Fermi surface that accounts for the long-range magnetic exchange by separating instantaneous and non-instantaneous gluon contributions, revealing a new RG flow for the $s$-wave channel that accelerates the approach to pairing. The main result is a superconducting gap scaling $Δ \sim μ g^{-5} \exp\left(-{3\pi^2\over\sqrt{2} g}\right)$—significantly larger at weak coupling than naïve $e^{-c/g^2}$ estimates—with the leading exponent confirmed by Eliashberg theory. The work also discusses the possibility of angular-momentum–carrying condensates and implications for intermediate densities, highlighting the role of dynamical (Landau) damping as the infrared cutoff in the pairing mechanism.

Abstract

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 $Δ$ at large chemical potential $μ$ qualitatively. We find $Δ\simμg^{-5}\exp(-{3π^2\over\sqrt{2}}{1\over g})$, 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.