Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography

Abstract

In this paper we obtain holographic formulas for the transport coefficients κ and τ π present in the second-order derivative expansion of relativistic hydrodynamics in curved spacetime associated with a non-conformal strongly coupled plasma described holographically by an Einstein+Scalar action in the bulk. We compute these coefficients as functions of the temperature in a bottom-up non-conformal model that is tuned to reproduce lattice QCD thermodynamics at zero baryon chemical potential. We directly compute, besides the speed of sound, 6 other transport coefficients that appear at second-order in the derivative expansion. We also give an estimate for the temperature dependence of 11 other transport coefficients taking into account the simplest contribution from non-conformal effects that appear near the QCD crossover phase transition. Using these results, we construct an Israel-Stewart-like theory in flat spacetime containing 13 of these 17 transport coefficients that should be suitable for phenomenological applications in the context of numerical hydrodynamic simulations of the strongly-coupled, non-conformal quark-gluon plasma. Using several different approximations, we give parametrizations for the temperature dependence of all the second-order transport coefficients that appear in this theory in a format that can be easily implemented in existing numerical hydrodynamic codes.

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“…vUSPhydro accurately [68] solves the energy-momentum conservation equations and the equations of motion for the dissipative currents using the Lagrangian formulation of hydrodynamics encoded in the Smoothed Particle Hydrodynamics (SPH) algorithm [69,70]. Information about four transport coe cients is required: the temperature-dependent shear and bulk viscosities, ⌘ and ⇣, and their respective relaxation time coe cients, ⌧ ⇡ and ⌧ ⇧ (other 2nd order transport coe cients [71] are not yet taken into account). For simplicity, e↵ects from the temperature dependence of ⌘/s in the hadronic [72][73][74] or in the QGP phase [75] are neglected here and, thus, we set ⌘/s to be a constant.…”

Dynamical versus equilibrium properties of the QCD phase transition: A holographic perspective

“…The quantity Λ is a scaling factor with dimensions of energy needed to convert observables computed on the gravity side to field theory units in MeV [59,60].…”

Vanishing DC holographic conductivity from a magnetic monopole condensate

“…Assuming spatial isotropy it follows that σ xx (ω) = σ yy (ω) ≡ σ(ω). 6 In order to calculate this retarded propagator we follow the holographic prescription proposed in [19], which was further justified and generalized in [20][21][22].…”

“…This has been extensively investigated in the last decade in the context of the strongly-coupled quark gluon plasma [4][5][6]. Recently, the holographic duality has been also used in the description of some properties of strongly correlated condensed matter systems, as reviewed in [7][8][9][10][11][12].…”