Dense Holographic QCD in the Wigner-Seitz Approximation

Abstract

We investigate cold dense matter in the context of Sakai and Sugimoto's holographic model of QCD in the Wigner-Seitz approximation. In bulk, baryons are treated as instantons on S^3\times R^1 in each Wigner-Seitz cell. In holographic QCD, Skyrmions are instanton holonomies along the conformal direction. The high density phase is identified with a crystal of holographic Skyrmions with restored chiral symmetry at about 4 Mkk^3/pi^5. As the average density goes up, it approaches to uniform distribution while the chiral condensate approaches to p-wave over a cell. The chiral symmetry is effectively restored in long wavelength limit since the chiral order parameter is averaged to be zero over a cell. The energy density in dense medium varies as n_B^{5/3}, which is the expected power for non-relativistic fermion. This shows that the Pauli exclusion effect in boundary is encoded in the Coulomb repulsion in the bulk.