Properties of Stable Massive Quark Stars in Holography

TL;DR

The paper investigates whether a holographic QCD model based on D3/D7 branes, with an infrared-modified dilaton, can yield a deconfined yet massive quark phase at finite density capable of forming quark-core compact stars. It demonstrates that, when paired with stiff Hebeler EFT baryonic EoS in a hybrid description, the quark phase can produce stable stars with $M_{\text{max}}$ up to about $2.17\,M_\odot$, though baryons modeled as wrapped D5-branes give unphysical pressures in the homogeneous limit. The quark matter phase exhibits a high polytropic index $\gamma(\epsilon)=\epsilon \frac{P'(\epsilon)}{P(\epsilon)}$ (up to $\sim 2.5$) and a rapid decrease in tidal deformability once a quark core forms, with the stiff baryonic phase causing tension with LIGO constraints. The study provides a proof-of-principle that holographic quark-star phenomenology is accessible in this framework, while highlighting the need for improved baryon-sector modeling and potential localization of D5-brane embeddings for a more definitive conclusion.

Abstract

We study a holographic D3/D7 system, whose dilaton profile has been phenomenologically adjusted in the infrared. The model is used to describe a deconfined yet massive quark phase of QCD at finite density, concluding that the equation of state of such a phase can be stiff enough to support exotic dense stars as massive as 2 solar masses. Nucleons are modeled phenomenologically using the Hebeler-et.al EFT baryon phases. For the stiff phenomenological baryon phases the transition to the quark phase is weakly first order allowing for stable quark cores. We also find that holographic baryons, modeled as wrapped D5-branes, provide unrealistic pressures (in the homogeneous approximation) and have to be discarded. We compute the mass vs. radius relation and tidal deformability for these hybrid stars. Contrary to a large number of other holographic models, this holographic model indicates that quark matter could be present at the core of heavy compact stars and may be used to explore the phenomenology of such objects.

Figures (10)

• Figure 1: The upper plot shows the embedding function $\chi(\rho)$ in the Minkowski (or vacuum) phase (blue) and the quark phase (black) for a generic value of $\mu$ at zero temperature. The lower plot shows the corresponding gauge potentials $A_t(\rho)$. The Minkowski phase has a chiral symmetry breaking vacuum but zero baryon density, while the quark phase restores chiral symmetry and has a nonzero $d$. All quantities are dimensionless and computed for a generic point in parameter space.
• Figure 2: Pressure $P$ as a function of the chemical potential for the quark phase defined with dilaton profile \ref{['eq:dil']} and range of parameters $\lambda_t=1.9...3$, $R_{\text{AdS}}= 0.015...0.02$ MeV$^{-1}$ (dashed black). The green curve corresponds to the basic D3/D7 model of Hoyos:2016zke . The reduced steepness of some of the the dashed black curves allows for a smoother transition from baryonic matter to quark matter ultimately enabling stars with quark cores when using the stiff Hebeler-et.al EoS for nucleon matter.
• Figure 3: The baryon vertex for $A=10,\tilde{\lambda}=1.715,\kappa=1$. All fundamental strings emerge from the pole at $\theta=\pi.$
• Figure 4: This figure compares the $P(\mu)$ behaviors of the $D5$ baryon phase (dashed red) to the phenomenological medium (in orange) and stiff (in red) phases of Hebeler:2013nza (we do not consider the soft EoS). The quark phase is shown in black for the parameter choice $A=10$, $\lambda=1.715$, $\kappa=1$, $\lambda_t=1.9$.
• Figure 5: Pressure as a function of chemical potential for the case of stiff (top) and medium (bottom) baryonic matter of Hebeler:2013nza, and quark matter (black and gray) of the holographic model described in section \ref{['quarkphase']}. The cases colored in black will support stable quark stars while the ones in gray will not. The parameter choices, which are described in section \ref{['sec:pars']}, are the same in both plots. The plots only differ in the description of the baryonic phase.