Transport properties of the quark-gluon plasma

Abstract

Abstract. Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.

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

“…Furthermore, another severe difficulty faced by lattice calculations concerns the computation of real-time, transport observables [43]. Relativistic hydrodynamics has been enormously successful in describing experimental observables with a small shear viscosity to entropy density ratio (η/s) and more recently with a bulk viscosity to entropy density ratio (ζ/s) exhibiting a peak at some characteristic temperature.…”

The shear channel spectral function in hot Yang-Mills theory

“…This suggests that if we define the momentum space shear channel correlator through 9) then in the → 0 limit the corresponding (p = 0) spectral function ρ η (ω) satisfies…”

“…[5,6]). At the same time, a reliable nonperturbative determination of transport coefficients, in principle available from the zero frequency limit of the corresponding (Minkowskian) spectral functions, has proven extremely challenging, as the lattice approach is restricted to the Euclidean formulation of the theory [7][8][9]. As a result, a considerable amount of attention has shifted towards the gauge/gravity duality, which has in particular led to the famous claim of the QGP being a nearly 'ideal' fluid, with a shear viscosity to entropy ratio close to the conjectured limit η/s ≥ 1/(4π) [10] (see also [11,12] for some interesting recent developments).…”

Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory

“…In the latter case, discussed extensively e.g. in [12], some progress has recently been made in combining lattice measurements of Euclidean correlators with perturbative results for the corresponding spectral functions [13,14]. Despite this, important hydrodynamic parameters such as the shear and bulk viscosities are still outside the realm of accurate first principles calculations.…”