Holographic (gauge/gravity-duality) models such as V-QCD, matched at low density to nuclear effective-field-theory equations of state and calibrated to lattice QCD at vanishing density, give a unified strong-coupling description of both nuclear and quark matter in neutron-star cores, and yield transport coefficients in the deconfined phase that differ qualitatively from perturbative-QCD (pQCD) extrapolations. As summarized in Jokela's 2021 NICER-era assessment and the program's 2022 review (Hoyos-Jokela-Vuorinen), this program is incomplete in several linked respects: the baryonic phase is treated in a homogeneous-baryon approximation whose failure at low density leaves the hybrid-construction matching density n_tr a free parameter whose variation induces a systematic uncertainty band; transport coefficients have been computed holographically only for unpaired deconfined quark matter, leaving the confined/baryonic and paired phases without any such results; finite-temperature extensions suited to neutron-star-merger conditions (T of order tens of MeV) are missing, while the currently available holographic-EoS merger simulations are ideal-fluid and the source cautions that any future simulations incorporating corrections beyond ideal fluid should proceed cautiously given the stark contrast with pQCD; and that contrast between holographic strong-coupling and pQCD predictions for transport and aspects of the equation of state (EoS) at intermediate densities is unresolved. The problem is to complete this description: extend the existing holographic results to a full set of EoS and transport coefficients for the confined/baryonic and paired phases at neutron-star and merger conditions from a single holographic framework matched to controlled limits, addressing the holography-versus-pQCD discrepancy at intermediate densities.

Background

Quantum Chromodynamics (QCD) at the baryon densities reached inside neutron stars is strongly coupled, so neither lattice simulation (which fails at finite baryon density because of the sign problem, the destructive interference of Monte-Carlo sampling weights at nonzero baryon chemical potential) nor perturbative QCD (pQCD, valid only at asymptotically high density) is controlled there; at low density, chiral effective field theory (EFT) describes nuclear matter. Neutron-star cores therefore probe a regime with no controlled first-principles method. The gauge/gravity duality (holography) maps certain strongly coupled gauge theories at large N (N being the number of color charges, taken large so that the dual gravity description is classical) onto classical gravity in one higher dimension, making hard field-theory questions tractable as general-relativity calculations; bottom-up holographic models such as V-QCD (a five-dimensional two-flavor model with a tachyon field encoding the spontaneous breaking of chiral symmetry, the approximate left-right symmetry of the light-quark sector) are tuned to reproduce lattice QCD thermodynamics at zero baryon density and then extrapolated to finite density. In V-QCD the nuclear-matter phase is described by a spatially homogeneous baryon charge distribution (the homogeneous-baryon approximation), which becomes unreliable at low densities; consequently one builds hybrid equations of state (EoS) by matching the holographic nuclear phase onto conventional nuclear-matter EoSs from EFT at a transition density n_tr, taken in the source work to lie in 1.2-2 n_s (n_s is nuclear saturation density, about 0.16 nucleons per cubic femtometer), with n_tr a free parameter whose variation induces a systematic uncertainty band. Inserting these hybrid EoSs in the Tolman-Oppenheimer-Volkoff equations for stellar structure and confronting them with radius measurements from NICER (the Neutron star Interior Composition Explorer, an X-ray timing telescope on the International Space Station), tidal-deformability limits from GW170817 (the binary-neutron-star merger observed in gravitational waves in 2017), and two-solar-mass pulsar masses, the source work concludes that neutron stars are fully hadronic without quark-matter cores - in tension with model-independent interpolation analyses such as Annala et al. (Nature Physics 2020) that favor quark matter in the most massive stars. Out of equilibrium, merger simulations suggest temperatures of several tens of MeV, requiring finite-temperature EoSs and transport coefficients (bulk and shear viscosities, heat and electric/thermal conductivities) that characterize how the matter dissipates perturbations. Transport coefficients are accessible in holography through linear-response (Kubo) computations on the gravity side, and this has been carried out for unpaired deconfined quark matter; the only first-principles alternative is leading-order pQCD. The two approaches disagree qualitatively at the intermediate densities relevant for neutron stars, and the source explicitly warns that merger simulations incorporating corrections beyond ideal hydrodynamics should proceed cautiously as a result. The program's own review (Hoyos-Jokela-Vuorinen 2022) adds that a nonzero temperature in the confined phase requires going beyond the large-N approximation, which has not been systematically implemented, and that a systematic study of paired (color-superconducting) phases - phases in which quarks form Cooper pairs near their Fermi surfaces, in analogy with ordinary superconductivity - and their influence on the EoS and transport properties is still lacking.

Problem Statement

Within a holographic framework that treats nuclear and quark matter in a unified way at strong coupling (such as V-QCD), matched at low densities to nuclear effective-field-theory equations of state and calibrated to lattice QCD at vanishing baryon density, complete the multi-phase description of dense QCD matter under neutron-star and binary-merger conditions by extending the existing holographic results - which cover transport coefficients only for unpaired deconfined quark matter - specifically: (1) the transport coefficients - bulk and shear viscosities and the heat and electric/thermal conductivities - of the confined/baryonic phase and of paired (color-superconducting) phases at temperatures of order tens of MeV, computed within the homogeneous-phase framework in which the hybrid construction and the existing transport computations are formulated (the possible instability of that framework to modulated phases being a stated difficulty; the framework denotes the spatially homogeneous setting, not a restriction to the leading large-N approximation, so beyond-large-N corrections are permitted where the finite-temperature confined-phase transport requires them); (2) the finite-temperature extension of the equation of state across these phases at merger-relevant temperatures of order tens of MeV, as microphysical input whose downstream use in merger modeling is motivated by the source's caution that simulations incorporating corrections beyond ideal fluid should proceed carefully given the holography-versus-pQCD contrast (the currently available holographic-EoS merger simulations being ideal-fluid); (3) an analysis, through these results, of the stark qualitative discrepancy between the holographic strong-coupling predictions and leading-order perturbative-QCD predictions for transport coefficients and for aspects of the equation of state (EoS) at the intermediate densities relevant for neutron stars, identifying where and why the two accounts diverge; and (4) reporting of the uncertainty band induced by the hybrid matching density n_tr (taken in the source work in 1.2-2 nuclear saturation densities, and varied over 1.2-2.6 in the companion construction), which remains a free parameter whose variation, together with the choice of nuclear model and the lattice-matching margin, produces that band. These components jointly serve one objective - a multi-phase holographic description of dense QCD matter ready for confrontation with neutron-star observations.

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