Color Superconductivity at Large N: A New Hope

TL;DR

This paper explores an alternative large N_c limit in QCD where color superconductivity at high densities remains plausible, potentially offering new insights into high-density QCD phenomena beyond the traditional large N_c approach.

Contribution

It introduces a different large N_c limit with quarks in the two-index antisymmetric representation, which avoids the DGR instability and supports the possibility of color superconductivity at large N_c.

Findings

DGR instability is absent in the alternative large N_c limit.

Color superconductivity may persist at large N_c in this new framework.

The new limit could provide useful insights into high-density QCD phenomena.

Abstract

At zero density, the `t Hooft large N_c limit often provides some very useful qualitative insights into the non-perturbative physics of QCD. However, it is known that at high densities the `t Hooft large N_c world looks very different from the N_c=3 world, which is believed to be in a color superconducting phase at high densities. At large N_c, on the other hand, the DGR instability causes a chiral-density wave phase to dominate over the color superconducting phase. There is an alternative large N_c limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at N_c=3 reduces to QCD but looks quite different at large N_c. We show that in this alternative large N_c limit, the DGR instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when N_c is large. This revives the hope that a large N_c approximation might be useful for getting some insights into the high-density phenomenology of QCD.