Dense matter in a holographic hard-wall model of QCD

TL;DR

This work develops a two-flavor holographic hard-wall model to study dense QCD matter at zero temperature and finite density, incorporating nonzero quark mass. Using a homogeneous ansatz, holographic renormalization, and IR boundary actions, it identifies a baryonic matter phase with nonzero density and suppressed chiral condensate, derives its equation of state, and computes neutron star mass–radius relations via the TOV equations. The results yield a stiff EOS with the speed of sound near the light speed limit and a maximum neutron-star mass above $2M_\odot$ for broad parameter choices, suggesting compatibility with heavy neutron-star observations; the study also discusses potential intermediate phases and limitations of the homogeneous-ansatz approach, and outlines future work to include strange quarks and axial-isovector condensates.

Abstract

A deeper understanding of QCD matter at strong coupling remains challenging due to its non-perturbative nature. To this end, we study a two-flavor holographic hard-wall model to investigate the properties of QCD at finite-density and zero temperature with a nonvanishing quark mass. A dense matter phase is described by a classical solution of the equations of motion in a homogeneous Ansatz. We apply holographic renormalization to formulate the holographic dictionary that relates UV boundary data in the bulk with the physical quantities in QCD. We emphasize a role played by an IR boundary action on the hard-wall when analyzing the QCD phase structures in this holographic setup. It is found that a baryonic matter phase is manifested in this model with a high baryon number density and a nearly vanishing chiral condensate. We derive the equation of state for the resulting phase and use it to work out the mass-radius relation for neutron stars. We find that the maximum mass of neutron stars can exceed two solar masses for a wide range of free parameters in this model. We also comment on an alternative scenario about the phase structure such that the baryonic matter phase arises at a baryon number chemical potential greater than a critical value.

Figures (12)

• Figure 1: The grand potential density as a function of $\mu_B$ at $L^{-1}=323\ \mathrm{MeV}$ (upper) and $L^{-1}=170\ \mathrm{MeV}$ (lower) for $k_2=5$ (left), $k_2=20$ (middle), and $k_2=35$ (right). Blue circles, orange triangles, and green diamonds are for $B = 0.4/L$, $0.6/L$, and $0.8/L$, respectively.
• Figure 2: The baryon number density around $\mu_B=1\ \mathrm{GeV}$ as a function of $\mu_B$ at $L^{-1}=323\ \mathrm{MeV}$ (upper) and $L^{-1}=170\ \mathrm{MeV}$ (lower) for $k_2=5$ (left), $k_2=20$ (middle), and $k_2=35$ (right). Blue circles, orange triangles and green diamonds are for $B = 0.4/L$, $0.6/L$ and $0.8/L$, respectively. The dashed lines represent the points closest to the critical point among the numerically calculated points.
• Figure 3: The baryon number density as a function of $\mu_B$ at $L^{-1}=323\ \mathrm{MeV}$ (upper) and $L^{-1}=170\ \mathrm{MeV}$ (lower) for $k_2=5$ (left), $k_2=20$ (middle), and $k_2=35$ (right). Blue circles, orange triangles and green diamonds are for $B = 0.4/L$, $0.6/L$ and $0.8/L$, respectively. The dashed lines represent the points closest to the critical point among the numerically calculated points.
• Figure 4: The chiral condensate normalized by the value in the nonbaryonic phase $\xi_0$ as a function of $\mu_B$ at $L^{-1}=323\ \mathrm{MeV}$ (upper) and $L^{-1}=170\ \mathrm{MeV}$ (lower) for $k_2=5$ (left), $k_2=20$ (middle), and $k_2=35$ (right). Blue circles, orange triangles and green diamonds are for $B = 0.4/L$, $0.6/L$ and $0.8/L$, respectively.
• Figure 5: The equation of state at $L^{-1}=323\ \mathrm{MeV}$ (upper) and $L^{-1}=170\ \mathrm{MeV}$ (lower) for $k_2=5$ (left), $k_2=20$ (middle), and $k_2=35$ (right). Blue circles, orange triangles and green diamonds are for $B = 0.4/L$, $0.6/L$ and $0.8/L$, respectively.