Holographic (gauge/gravity) methods currently provide the only systematic strong-coupling predictions for the transport coefficients of dense quark matter in the neutron-star regime, but the existing computation assumes unpaired, three-flavor, flavor-degenerate quark matter in beta equilibrium without leptons, with the quark masses set to zero in the V-QCD model and kept nonzero in the D3-D7 model. This problem asks for the realistic extension of that calculation: determine the shear viscosity, bulk viscosity, electrical conductivity, and thermal conductivity of strongly coupled dense quark matter when color-superconducting quark pairing, flavor-dependent quark masses with leptons imposed by charge neutrality, and the backreaction of dynamical flavors (beyond the quenched probe-brane approximation) are included. The weak-interaction (Urca-type) contribution to the bulk viscosity of unpaired matter, flagged as an open issue in the original work, has since been addressed by separate perturbative-plus-holographic calculations and is not part of the requested core; the bulk viscosity sought here is the strongly coupled QCD contribution computed holographically, as in the original work.

Background

At the densities reached in neutron-star cores and binary merger remnants, deconfined quark matter — if present — is too strongly coupled for perturbation theory and, at nonzero baryon chemical potential, inaccessible to lattice QCD because of the fermion sign problem (exponentially severe cancellations between positive- and negative-weight gauge-field configurations at nonzero baryon chemical potential). Its transport coefficients nevertheless matter astrophysically: the shear viscosity η\eta and bulk viscosity ζ\zeta control the damping of density oscillations and of r-modes (rotation-driven oscillation modes of neutron stars whose amplification is limited by viscous damping), while the electrical conductivity σ\sigma and thermal conductivity κ\kappa govern magnetic-field and heat transport in merger simulations. At weak coupling these coefficients are computed perturbatively from quark quasiparticle scattering, but the relevant coupling is not small. The gauge/gravity duality (holography) maps certain strongly coupled gauge theories onto classical gravity in one higher dimension: transport coefficients are extracted from horizon data of the dual black-hole geometry or from Kubo formulas (linear-response relations expressing transport coefficients in terms of current- and stress-tensor two-point correlators at zero frequency and momentum). The bottom-up 'V-QCD' construction models large-NcN_c QCD with dynamical (unquenched) flavors via a five-dimensional dilaton-gravity action fitted to lattice Yang-Mills data and perturbative QCD, while the top-down D3-D7 model describes quenched flavor branes probing an AdS5×S5AdS_5\times S^5 black hole, with flavor backreaction suppressed at small Nf/NcN_f/N_c. In the D3-D7 setup a nonzero quark mass breaks conformal invariance and generates a nonzero ζ\zeta; in V-QCD the same role is played by the running dilaton. Color superconductivity is the expected ground state of sufficiently cold dense quark matter: attractive gluon exchange pairs quarks (as in BCS superconductivity), producing phases such as the two-flavor color-superconducting (2SC) phase and the color-flavor-locked (CFL) phase, with pairing gaps that are exponentially uncertain at neutron-star densities. Beta equilibrium — the balance of chemical potentials maintained by weak flavor-changing processes, such as the Urca-type reactions u+d↔u+su+d\leftrightarrow u+s and u+e−↔d+νeu+e^-\leftrightarrow d+\nu_e — fixes the composition together with electric charge neutrality, which forces a small lepton fraction. In 2020, Hoyos, Järvinen, Jokela, Subils, Tarrío, and Vuorinen (Phys. Rev. Lett. 125, 241601) used V-QCD and the quenched D3-D7 model to compute η\eta, ζ\zeta, σ\sigma, and κ\kappa for unpaired quark matter of three degenerate flavors (massless in V-QCD, with a nonzero degenerate quark mass in D3-D7) in beta equilibrium without electrons. They found dramatic qualitative disagreement with perturbative QCD (coefficients increasing rather than decreasing with temperature at low TT), and they identified the physical ingredients their calculation deliberately omitted: quark pairing, flavor-dependent masses and leptons, the weak-process contribution to ζ\zeta (which they estimated from earlier weak-coupling work to dominate, ζ∼1024−1029 g cm−1 s−1\zeta\sim 10^{24}-10^{29}\,\mathrm{g\,cm^{-1}\,s^{-1}}), and the unquenched treatment of the D3-D7 conductivities. A longer companion paper (Phys. Rev. D 105, 066014 (2022)) confirmed that no results exist for the paired ('color superconducting') phases and expressed the expectation that similar strong-coupling effects arise there.

Problem Statement

Determine the transport coefficients of strongly coupled dense quark matter — the shear viscosity η\eta, the bulk viscosity ζ\zeta, the electrical conductivity σ\sigma, and the thermal conductivity κ\kappa — under the realistic conditions that the original holographic calculation (Hoyos et al., Phys. Rev. Lett. 125, 241601 (2020)) omitted. The common objective is a usable strong-coupling prediction of dense-quark-matter transport for neutron-star physics, generalizing the unpaired, flavor-degenerate baseline. Concretely: (i) compute the transport coefficients of paired (color-superconducting) phases of strongly coupled dense quark matter; (ii) compute the coefficients with realistic flavor structure — flavor-dependent quark masses (such as a 2+1-flavor setup with a massive strange quark) and leptons imposed by charge neutrality and beta equilibrium — and quantify the changes relative to the flavor-degenerate three-flavor baseline; (iii) quantify the effect of flavor backreaction on the transport coefficients of the D3-D7 system beyond the quenched probe-brane approximation, and compare the resulting coefficients with the V-QCD predictions. Sub-questions (i)–(iii) stand independently and all three form the single objective above. The coefficients are sought as functions of temperature and baryon chemical potential over the neutron-star-relevant regime, together with their comparison to the corresponding weak-coupling predictions from perturbative QCD. The weak-interaction (Urca-type) contribution to the bulk viscosity of unpaired matter has been addressed by separate 2024 calculations and lies outside the requested core; the bulk viscosity sought here is the strongly coupled QCD (holographic) contribution.

References

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  2. C. Hoyos, N. Jokela, M. Järvinen, J. G. Subils, J. Tarrío, and A. Vuorinen, 'Holographic approach to transport in dense QCD matter', Phys. Rev. D 105, 066014 (2022). DOI: 10.1103/PhysRevD.105.066014, https://arxiv.org/abs/2109.12122
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