Cold Nuclear Matter In Holographic QCD

TL;DR

This paper analyzes zero-temperature QCD-like dynamics at finite baryon chemical potential using the Sakai-Sugimoto holographic model. It demonstrates a first-order transition to an inhomogeneous nuclear-matter phase with an instanton-density condensate on the D8-branes, whose UV expansion with increasing $\mu$ provides a holographic analogue of Fermi-surface expansion and connects to the large-$N_c$ chiral density wave. The work further develops both one- and two-flavor sectors, showing that homogeneous configurations are insufficient and that inhomogeneity is intrinsic in the large-$N_c$ limit; it also offers a semi-quantitative prediction for the binding energy per nucleon in ordinary QCD by analyzing the $\lambda$-dependence of $\mu_c$ and $M_B$. Overall, the results illuminate how nuclear matter and baryon binding emerge in holographic QCD and provide a framework to estimate nuclear properties from first principles in the strong-coupling regime.

Abstract

We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density. This suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large N_c QCD at asymptotically large chemical potential. We study properties of the nuclear matter phase as a function of chemical potential beyond the transition and argue in particular that the model can be used to make a semi-quantitative prediction of the binding energy per nucleon for nuclear matter in ordinary QCD.

Figures (1)

• Figure 1: Type IIA string theory configuration for the Sakai-Sugimoto model.