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Holography and Fermions at a Finite Chemical Potential

We review the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential, comparing the results to those expected at large-$N_c$ QCD, and those in a closely related holographic model. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase, the details of which depend on the model. We argue that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density, which suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large-$N_c$ QCD. Some details of the instanton distribution in the holographic dual are reminiscent of a Fermi surface. This short manuscript summarizes a talk given by M.R. at "Theory Canada 4" conference, and is based largely (but not entirely) on the results of \cite{Rozalietal2008}.