Properties of Stable Massive Quark Stars in Holography

Author(s)

Bitaghsir Fadafan, Kazem, Cruz Rojas, Jesús, Mager, Jonas

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

\footnotesize{ 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.}
Caption \footnotesize{ 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.}
\footnotesize{ 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.}
Caption \footnotesize{ 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.}
Pressure $P$ as a function of the chemical potential for the quark phase defined with dilaton profile \eqref{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 \cite{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.
Caption Pressure $P$ as a function of the chemical potential for the quark phase defined with dilaton profile \eqref{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 \cite{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.
\footnotesize{ { The baryon vertex for $A=10,\tilde{\lambda}=1.715,\kappa=1$. All fundamental strings emerge from the pole at $\theta=\pi.$}}
Caption \footnotesize{ { The baryon vertex for $A=10,\tilde{\lambda}=1.715,\kappa=1$. All fundamental strings emerge from the pole at $\theta=\pi.$}}
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 \cite{Hebeler:2013nza} (we do not consider the soft EoS). The quark phase is shown in black for the parameter choice $A=10$, $\lambda=1.715$, $\kappa=1$, $\lambda_t=1.9$.
Caption 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 \cite{Hebeler:2013nza} (we do not consider the soft EoS). The quark phase is shown in black for the parameter choice $A=10$, $\lambda=1.715$, $\kappa=1$, $\lambda_t=1.9$.
Pressure as a function of chemical potential for the case of stiff (top) and medium (bottom) baryonic matter of \cite{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.
Caption Pressure as a function of chemical potential for the case of stiff (top) and medium (bottom) baryonic matter of \cite{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.
Pressure as a function of chemical potential for the case of stiff (top) and medium (bottom) baryonic matter of \cite{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.
Caption Pressure as a function of chemical potential for the case of stiff (top) and medium (bottom) baryonic matter of \cite{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.
Collection of equations of state in a pressure vs. energy density plot for stiff and medium baryonic phases. Color coding and line styles are as in fig \ref{pressure2}. Phase transitions are indicated by dashed grey lines. The quark phases all asymptote to the pQCD regime. {The gray region found in \cite{Annala:2017llu} is consistent with pQCD and astrophysical constraints.}
Caption Collection of equations of state in a pressure vs. energy density plot for stiff and medium baryonic phases. Color coding and line styles are as in fig \ref{pressure2}. Phase transitions are indicated by dashed grey lines. The quark phases all asymptote to the pQCD regime. {The gray region found in \cite{Annala:2017llu} is consistent with pQCD and astrophysical constraints.}
Collection of equations of state in a pressure vs. energy density plot for stiff and medium baryonic phases. Color coding and line styles are as in fig \ref{pressure2}. Phase transitions are indicated by dashed grey lines. The quark phases all asymptote to the pQCD regime. {The gray region found in \cite{Annala:2017llu} is consistent with pQCD and astrophysical constraints.}
Caption Collection of equations of state in a pressure vs. energy density plot for stiff and medium baryonic phases. Color coding and line styles are as in fig \ref{pressure2}. Phase transitions are indicated by dashed grey lines. The quark phases all asymptote to the pQCD regime. {The gray region found in \cite{Annala:2017llu} is consistent with pQCD and astrophysical constraints.}
The speed of sound for the 3 equations of state that allow for stable quark matter cores. Dashed gray lines indicate phase transitions to the quark phases, which in this plot lie on top of each other and approach a value smaller than the conformal $\frac{1}{3}$ (indicated as a vertical dotted gray line) in the UV.
Caption The speed of sound for the 3 equations of state that allow for stable quark matter cores. Dashed gray lines indicate phase transitions to the quark phases, which in this plot lie on top of each other and approach a value smaller than the conformal $\frac{1}{3}$ (indicated as a vertical dotted gray line) in the UV.
The polytropic index $\gamma$ for the 3 equations of state that allow for stable quark matter cores as a function of the normalised density $\frac{n}{n_{\text{sat}}}$. Dashed gray lines indicate phase transitions to the quark phases. At large densities, the graphs are slightly below the conformal value of $\gamma=1$.
Caption The polytropic index $\gamma$ for the 3 equations of state that allow for stable quark matter cores as a function of the normalised density $\frac{n}{n_{\text{sat}}}$. Dashed gray lines indicate phase transitions to the quark phases. At large densities, the graphs are slightly below the conformal value of $\gamma=1$.
Mass vs radius curves for stiff (top) and medium (bottom) phenomenological baryon phases together with the holographic quark phase. The quark phases highlighted in gray do not lead to stable quark matter in the core, whilst the 3 curves in black in the upper plot support quark stars as high as $M=2.17\, M_\odot$. As mentioned in the text, the stiff baryonic phase is crucial.
Caption Mass vs radius curves for stiff (top) and medium (bottom) phenomenological baryon phases together with the holographic quark phase. The quark phases highlighted in gray do not lead to stable quark matter in the core, whilst the 3 curves in black in the upper plot support quark stars as high as $M=2.17\, M_\odot$. As mentioned in the text, the stiff baryonic phase is crucial.
Mass vs radius curves for stiff (top) and medium (bottom) phenomenological baryon phases together with the holographic quark phase. The quark phases highlighted in gray do not lead to stable quark matter in the core, whilst the 3 curves in black in the upper plot support quark stars as high as $M=2.17\, M_\odot$. As mentioned in the text, the stiff baryonic phase is crucial.
Caption Mass vs radius curves for stiff (top) and medium (bottom) phenomenological baryon phases together with the holographic quark phase. The quark phases highlighted in gray do not lead to stable quark matter in the core, whilst the 3 curves in black in the upper plot support quark stars as high as $M=2.17\, M_\odot$. As mentioned in the text, the stiff baryonic phase is crucial.
The dimensionless tidal deformability $\Lambda$ as a function of the mass of the star. After the transition from the phenomenological stiff phase (in red) to the quark matter in the core (in black) the tidal deformability decreases rather rapidly.
Caption The dimensionless tidal deformability $\Lambda$ as a function of the mass of the star. After the transition from the phenomenological stiff phase (in red) to the quark matter in the core (in black) the tidal deformability decreases rather rapidly.
References
  • [1] D. D. Ivanenko and D. F. Kurdgelaidze, Hypothesis concerning quark stars, Astrophysics 1 (1965) 251–252.
  • [2] N. Itoh, Hydrostatic Equilibrium of Hypothetical Quark Stars, Prog. Theor. Phys. 44 (1970) 291.
  • [3] C. Alcock, E. Farhi, and A. Olinto, Strange stars, Astrophys. J. 310 (1986) 261–272.
  • [4] E. Witten, Cosmic Separation of Phases, Phys. Rev. D 30 (1984) 272–285.
  • [5] E. Annala, T. Gorda, J. Hirvonen, O. Komoltsev, A. Kurkela, J. Nättilä, and A. Vuorinen, Strongly interacting matter exhibits deconfined behavior in massive neutron stars, Nature Commun. 14 (2023), no. 1 8451, [arXiv:2303.11356].
  • [6] E. S. Fraga, R. D. Pisarski, and J. Schaffner-Bielich, Small, dense quark stars from perturbative QCD, Phys. Rev. D 63 (2001) 121702, [hep-ph/0101143].
  • [7] A. Kurkela, P. Romatschke, A. Vuorinen, and B. Wu, Looking inside neutron stars: Microscopic calculations confront observations, arXiv:1006.4062.
  • [8] F. Köpp, J. E. Horvath, D. Hadjimichef, and C. A. Z. Vasconcellos, Quark/Hybrid Stars Within Perturbative QCD in View of the GW170817 Event, Astron. Nachr. 346 (2025), no. 3-4 e20240136.
  • [9] LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017), no. 16 161101, [arXiv:1710.05832].
  • [10] P. Demorest, T. Pennucci, S. Ransom, M. Roberts, and J. Hessels, Shapiro Delay Measurement of A Two Solar Mass Neutron Star, Nature 467 (2010) 1081–1083, [arXiv:1010.5788].
  • [11] J. Antoniadis et al., A Massive Pulsar in a Compact Relativistic Binary, Science 340 (2013) 6131, [arXiv:1304.6875].
  • [12] E. Fonseca et al., The NANOGrav Nine-year Data Set: Mass and Geometric Measurements of Binary Millisecond Pulsars, Astrophys. J. 832 (2016), no. 2 167, [arXiv:1603.00545].
  • [13] NANOGrav Collaboration, H. T. Cromartie et al., Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar, Nature Astron. 4 (2019), no. 1 72–76, [arXiv:1904.06759].
  • [14] E. Fonseca et al., Refined Mass and Geometric Measurements of the High-mass PSR J0740+6620, Astrophys. J. Lett. 915 (2021), no. 1 L12, [arXiv:2104.00880].
  • [15] J. Nättilä, M. C. Miller, A. W. Steiner, J. J. E. Kajava, V. F. Suleimanov, and J. Poutanen, Neutron star mass and radius measurements from atmospheric model fits to X-ray burst cooling tail spectra, Astron. Astrophys. 608 (2017) A31, [arXiv:1709.09120].
  • [16] M. C. Miller et al., PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter, Astrophys. J. Lett. 887 (2019), no. 1 L24, [arXiv:1912.05705].
  • [17] M. C. Miller et al., The Radius of PSR J0740+6620 from NICER and XMM-Newton Data, Astrophys. J. Lett. 918 (2021), no. 2 L28, [arXiv:2105.06979].
  • [18] M. Evans et al., A Horizon Study for Cosmic Explorer: Science, Observatories, and Community, arXiv:2109.09882.
  • [19] ET Collaboration, A. Abac et al., The Science of the Einstein Telescope, arXiv:2503.12263.
  • [20] A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, and V. F. Weisskopf, A New Extended Model of Hadrons, Phys. Rev. D 9 (1974) 3471–3495.
  • [21] K. Yagi and N. Yunes, Approximate Universal Relations for Neutron Stars and Quark Stars, Phys. Rept. 681 (2017) 1–72, [arXiv:1608.02582].
  • [22] J. Leutgeb, J. Mager, and A. Rebhan, Hadronic light-by-light contribution to the muon g-2 from holographic QCD with solved U(1)A problem, Phys. Rev. D 107 (2023), no. 5 054021, [arXiv:2211.16562].
  • [23] J. Leutgeb, J. Mager, and A. Rebhan, Superconnections in AdS/QCD and the hadronic light-by-light contribution to the muon g-2, Phys. Rev. D 111 (2025), no. 11 114001, [arXiv:2411.10432].
  • [24] L. Cappiello, J. Leutgeb, J. Mager, and A. Rebhan, Tensor meson transition form factors in holographic QCD and the muon g − 2, JHEP 07 (2025) 033, [arXiv:2501.09699].
  • [25] J. Mager, L. Cappiello, J. Leutgeb, and A. Rebhan, Longitudinal Short-Distance Constraints on Hadronic Light-by-Light Scattering and Tensor-Meson Contributions to the Muon g-2, Phys. Rev. Lett. 135 (2025), no. 9 091901, [arXiv:2501.19293].
  • [26] E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505–532, [hep-th/9803131].
  • [27] A. Karch and E. Katz, Adding flavor to AdS / CFT, JHEP 06 (2002) 043, [hep-th/0205236].
  • [28] T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843–882, [hep-th/0412141].
  • [29] T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083–1118, [hep-th/0507073].
  • [30] J. Leutgeb, J. Mager, and A. Rebhan, Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model, arXiv:2511.11797.
  • [31] J. Erlich, E. Katz, D. T. Son, and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602, [hep-ph/0501128].
  • [32] L. Da Rold and A. Pomarol, Chiral symmetry breaking from five dimensional spaces, Nucl. Phys. B 721 (2005) 79–97, [hep-ph/0501218].
  • [33] A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005, [hep-ph/0602229].
  • [34] M. Jarvinen and E. Kiritsis, Holographic Models for QCD in the Veneziano Limit, JHEP 03 (2012) 002, [arXiv:1112.1261].
  • [35] K. Bitaghsir Fadafan, J. Cruz Rojas, and N. Evans, Deconfined, Massive Quark Phase at High Density and Compact Stars: A Holographic Study, Phys. Rev. D 101 (2020), no. 12 126005, [arXiv:1911.12705].
  • [36] K. Bitaghsir Fadafan, J. Cruz Rojas, and N. Evans, Holographic quark matter with colour superconductivity and a stiff equation of state for compact stars, Phys. Rev. D 103 (2021), no. 2 026012, [arXiv:2009.14079].
  • [37] N. Evans, A. Gebauer, K.-Y. Kim, and M. Magou, Holographic Description of the Phase Diagram of a Chiral Symmetry Breaking Gauge Theory, JHEP 03 (2010) 132, [arXiv:1002.1885].
  • [38] S. S. Gubser, Dilaton driven confinement, hep-th/9902155.
  • [39] N. R. Constable and R. C. Myers, Exotic scalar states in the AdS / CFT correspondence, JHEP 11 (1999) 020, [hep-th/9905081].
  • [40] J. Babington, J. Erdmenger, N. J. Evans, Z. Guralnik, and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007, [hep-th/0306018].
  • [41] M. Atashi and K. Bitaghsir Fadafan, Anomalous dimension and quasinormal modes of flavor branes, Annals Phys. 469 (2024) 169762.
  • [42] K. Bitaghsir Fadafan and M. Gholamzadeh, Chiral Symmetry Breaking and the Critical Point in QCD-like Theories, JHAP 4 (2024), no. 3 19–34.
  • [43] M. Ahmadvand, A. Ashoorioon, and K. Bitaghsir Fadafan, Confronting the magnetically-induced holographic composite inflation with observation, Phys. Rev. D 104 (2021), no. 6 063509, [arXiv:2103.08362].
  • [44] O. Bergman, G. Lifschytz, and M. Lippert, Holographic Nuclear Physics, JHEP 11 (2007) 056, [arXiv:0708.0326].
  • [45] M. Rozali, H.-H. Shieh, M. Van Raamsdonk, and J. Wu, Cold Nuclear Matter In Holographic QCD, JHEP 01 (2008) 053, [arXiv:0708.1322].
  • [46] K.-Y. Kim, S.-J. Sin, and I. Zahed, Dense holographic QCD in the Wigner-Seitz approximation, JHEP 09 (2008) 001, [arXiv:0712.1582].
  • [47] V. Kaplunovsky, D. Melnikov, and J. Sonnenschein, Baryonic Popcorn, JHEP 11 (2012) 047, [arXiv:1201.1331].
  • [48] S.-w. Li, A. Schmitt, and Q. Wang, From holography towards real-world nuclear matter, Phys. Rev. D 92 (2015), no. 2 026006, [arXiv:1505.04886].
  • [49] M. Elliot-Ripley, P. Sutcliffe, and M. Zamaklar, Phases of kinky holographic nuclear matter, JHEP 10 (2016) 088, [arXiv:1607.04832].
  • [50] N. Kovensky and A. Schmitt, Holographic quarkyonic matter, JHEP 09 (2020) 112, [arXiv:2006.13739].
  • [51] F. Preis and A. Schmitt, Layers of deformed instantons in holographic baryonic matter, JHEP 07 (2016) 001, [arXiv:1606.00675].
  • [52] K. Bitaghsir Fadafan, F. Kazemian, and A. Schmitt, Towards a holographic quark-hadron continuity, JHEP 03 (2019) 183, [arXiv:1811.08698].
  • [53] N. Kovensky, A. Poole, and A. Schmitt, Building a realistic neutron star from holography, Phys. Rev. D 105 (2022), no. 3 034022, [arXiv:2111.03374].
  • [54] L. Bartolini and S. B. Gudnason, Neutron stars in the Witten-Sakai-Sugimoto model, JHEP 11 (2023) 209, [arXiv:2307.11886].
  • [55] N. Jokela, M. Järvinen, and J. Remes, Holographic QCD in the Veneziano limit and neutron stars, JHEP 03 (2019) 041, [arXiv:1809.07770].
  • [56] P. M. Chesler, N. Jokela, A. Loeb, and A. Vuorinen, Finite-temperature Equations of State for Neutron Star Mergers, Phys. Rev. D 100 (2019), no. 6 066027, [arXiv:1906.08440].
  • [57] C. Ecker, M. Järvinen, G. Nijs, and W. van der Schee, Gravitational waves from holographic neutron star mergers, Phys. Rev. D 101 (2020), no. 10 103006, [arXiv:1908.03213].
  • [58] N. Jokela, M. Järvinen, G. Nijs, and J. Remes, Unified weak and strong coupling framework for nuclear matter and neutron stars, Phys. Rev. D 103 (2021), no. 8 086004, [arXiv:2006.01141].
  • [59] M. Järvinen, Holographic modeling of nuclear matter and neutron stars, Eur. Phys. J. C 82 (2022), no. 4 282, [arXiv:2110.08281].
  • [60] M. Jarvinen, Holographic baryons, dense matter and neutron star mergers, JHAP 3 (2023), no. 3 1–22, [arXiv:2307.01745].
  • [61] L. Bartolini, S. B. Gudnason, and M. Järvinen, Isospin asymmetry and neutron stars in holographic QCD in the Veneziano limit, Phys. Rev. D 111 (2025), no. 10 106021, [arXiv:2504.01758].
  • [62] L. Bartolini, S. B. Gudnason, J. Leutgeb, and A. Rebhan, Neutron stars and phase diagram in a hard-wall AdS/QCD model, Phys. Rev. D 105 (2022), no. 12 126014, [arXiv:2202.12845].
  • [63] L. Zhang and M. Huang, Holographic cold dense matter constrained by neutron stars, Phys. Rev. D 106 (2022), no. 9 096028, [arXiv:2209.00766].
  • [64] C. Hoyos, D. Rodrı́guez Fernández, N. Jokela, and A. Vuorinen, Holographic quark matter and neutron stars, Phys. Rev. Lett. 117 (2016), no. 3 032501, [arXiv:1603.02943].
  • [65] M. Aleixo, C. H. Lenzi, W. de Paula, and R. da Rocha, Quark stars in D3–D7 holographic model, Eur. Phys. J. C 84 (2024), no. 3 253, [arXiv:2310.17719].
  • [66] A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: Some exact results, JHEP 11 (2007) 074, [arXiv:0709.0570].
  • [67] E. Annala, T. Gorda, A. Kurkela, and A. Vuorinen, Gravitational-wave constraints on the neutron-star-matter Equation of State, Phys. Rev. Lett. 120 (2018), no. 17 172703, [arXiv:1711.02644].
  • [68] K. Hebeler, J. M. Lattimer, C. J. Pethick, and A. Schwenk, Equation of state and neutron star properties constrained by nuclear physics and observation, Astrophys. J. 773 (2013) 11, [arXiv:1303.4662].
  • [69] N. Evans, K.-Y. Kim, M. Magou, Y. Seo, and S.-J. Sin, The Baryonic Phase in Holographic Descriptions of the QCD Phase Diagram, JHEP 09 (2012) 045, [arXiv:1204.5640].
  • [70] B. Gwak, M. Kim, B.-H. Lee, Y. Seo, and S.-J. Sin, Holographic D Instanton Liquid and chiral transition, Phys. Rev. D 86 (2012) 026010, [arXiv:1203.4883].
  • [71] M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023, [hep-th/9806087].
  • [72] M. Hippert, J. Noronha, and P. Romatschke, Upper bound on the speed of sound in nuclear matter from transport, Phys. Lett. B 860 (2025) 139184, [arXiv:2402.14085].
  • [73] E. Annala, T. Gorda, A. Kurkela, J. Nättilä, and A. Vuorinen, Evidence for quark-matter cores in massive neutron stars, Nature Phys. 16 (2020), no. 9 907–910, [arXiv:1903.09121].
  • [74] E. Annala, T. Gorda, E. Katerini, A. Kurkela, J. Nättilä, V. Paschalidis, and A. Vuorinen, Multimessenger Constraints for Ultradense Matter, Phys. Rev. X 12 (2022), no. 1 011058, [arXiv:2105.05132].
  • [75] P. Haensel, A. Y. Potekhin, and D. G. Yakovlev, Neutron stars 1: Equation of state and structure, vol. 326. Springer, New York, USA, 2007.
  • [76] M. Albino, T. Malik, M. Ferreira, and C. Providência, A Bayesian Inference of Hybrid Stars with Large Quark Cores, arXiv:2511.02653.
  • [77] E. E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77 (2008) 021502, [arXiv:0709.1915].
  • [78] T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral, Phys. Rev. D 81 (2010) 123016, [arXiv:0911.3535].
  • [79] S. Postnikov, M. Prakash, and J. M. Lattimer, Tidal Love Numbers of Neutron and Self-Bound Quark Stars, Phys. Rev. D 82 (2010) 024016, [arXiv:1004.5098].
  • [80] T. Zhao and J. M. Lattimer, Tidal Deformabilities and Neutron Star Mergers, Phys. Rev. D 98 (2018), no. 6 063020, [arXiv:1808.02858].
  • [81] J. Takátsy and P. Kovács, Comment on ”Tidal Love numbers of neutron and self-bound quark stars”, Phys. Rev. D 102 (2020), no. 2 028501, [arXiv:2007.01139].
  • [82] S. Han and A. W. Steiner, Tidal deformability with sharp phase transitions in (binary) neutron stars, Phys. Rev. D 99 (2019), no. 8 083014, [arXiv:1810.10967].
  • [83] A. Guerra Chaves and T. Hinderer, Probing the equation of state of neutron star matter with gravitational waves from binary inspirals in light of GW170817: a brief review, J. Phys. G 46 (2019), no. 12 123002, [arXiv:1912.01461].
  • [84] LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121 (2018), no. 16 161101, [arXiv:1805.11581].
  • [85] E. Annala, C. Ecker, C. Hoyos, N. Jokela, D. Rodrı́guez Fernández, and A. Vuorinen, Holographic compact stars meet gravitational wave constraints, JHEP 12 (2018) 078, [arXiv:1711.06244].