At zero density, the ‘t Hooft large $N_c$ limit often provides some very useful qualitative insights into the nonperturbative 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 Deryagin, Grigoriev, and Rubakov 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 Deryagin, Grigoriev, and Rubakov 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.

• Received 27 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.125021