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

TL;DR

This paper derives holographic formulas for second-order transport coefficients in a non-conformal quark-gluon plasma, providing temperature-dependent values and a practical framework for hydrodynamic simulations relevant to QCD phenomenology.

Contribution

It introduces new holographic formulas for second-order transport coefficients in non-conformal plasmas, with explicit temperature dependence and a comprehensive set of coefficients for hydrodynamic modeling.

Findings

Computed six second-order transport coefficients as functions of temperature.

Provided estimates for temperature dependence of eleven additional coefficients.

Constructed an Israel-Stewart-like hydrodynamic theory with 13 transport coefficients.

Abstract

In this paper we obtain holographic formulas for the transport coefficients $\kappa$ and $\tau_\pi$ 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.