Question

I am sending a couple of questions which seem a bit more specific than others on this site, partially to probe if there is a point in doing so. Not sure what is the range of expertise here, and no way to find out without trying, so here goes:

I am wondering what is known about QCD, or other field theories, in the regime of large density and low temperatures, specifically studied in the large N limit. I know of the qualitative picture at finite N, but lots of the instabilities (e.g. the superconducting ones) are suppressed at large N and replaced by other interesting phenomena. I am only aware at the moment of the DGR instability to form chiral density waves, and I am wondering what else exists in the vast and possibly quite old literature. Any pointers or entry points to that literature will be appreciated

Answer 1

If by large density you mean large baryon density, then I believe one of the fundamental large results is that at densities of order nuclear densities, but below the density where the baryons have dissolved into quarks, baryonic matter forms a crystalline structure. This has been analyzed in the Skyrme model. I think this paper by Klebanov was one of the first to point this out: "Nuclear Matter In The Skyrme Model,"Igor R. Klebanov, Nucl.Phys.B262:133,1985.

AdS/QCD models can also be used to study QCD at large baryon chemical potential and low temperatures (and necessarily at large ). An instability to the condensation of vector mesons resulting from Chern-Simons couplings dictated by anomaly matching was found in a paper by me and S. Domokos, arXiv:0704.1604. I'm not aware of any evidence that this phenomenon happens in the real world, and even its existence at large should be regarded as conjectural. I don't know whether this instability is related to the DGR instability or not.