Color superconductivity at large N: A new hope

Abstract

At zero density, the ‘t Hooft large Nc 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 Nc world looks very different from the Nc=3 world, which is believed to be in a color-superconducting phase at high densities. At large Nc, 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 Nc limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at Nc=3 reduces to QCD but looks quite different at large Nc. We show that in this alternative large Nc 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 Nc is large. This revives the hope that a large Nc approximation might be useful for getting some insights into the high-density phenomenology of QCD.

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