Dense Holographic QCD in the Wigner-Seitz Approximation

TL;DR

This paper explores dense baryonic matter using holographic QCD, modeling baryons as instantons in a Wigner-Seitz cell, revealing chiral symmetry restoration and fermionic behavior at high densities.

Contribution

It introduces a holographic model of dense matter with instantons in the Wigner-Seitz approximation, demonstrating chiral symmetry restoration and fermionic energy scaling.

Findings

Chiral symmetry is effectively restored at high density.

Energy density scales as n_B^{5/3}, indicating fermionic behavior.

Chiral condensate approaches zero in the long wavelength limit.

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.