Holography and Fermions at a Finite Chemical Potential

TL;DR

This paper reviews holographic QCD models at finite chemical potential, highlighting a phase transition to inhomogeneous nuclear matter and suggesting a connection to Fermi surface instabilities in large-N_c QCD.

Contribution

It demonstrates the occurrence of inhomogeneous nuclear matter phases in holographic models and links these to Fermi surface phenomena in large-N_c QCD.

Findings

Phase transition to nuclear matter at critical chemical potential.

Inhomogeneous nuclear matter persists at high densities.

Holographic instanton distributions resemble Fermi surface features.

Abstract

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}.