Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective

TL;DR

This review surveys how lattice QCD can determine the transport properties of the quark-gluon plasma by focusing on Euclidean current correlators and their spectral functions through Kubo relations. It contrasts hydrodynamic, kinetic, perturbative, and holographic perspectives to assess whether the QGP behaves as a weakly coupled quasiparticle gas or a strongly coupled fluid. A central challenge is the ill-posed analytic continuation from Euclidean data to real-time spectra, which is tackled with linear methods, maximum entropy, and hybrid approaches while leveraging sum rules and OPE constraints. The work highlights the significant computational demands and outlines concrete paths for achieving decisive results, with implications for heavy-ion phenomenology and early-universe cosmology.

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.

Figures (37)

• Figure 1: The response of nuclear matter to an anisotropic initial condition in configuration space, expressed as the elliptic flow $v_2(p_t)$ per unit excentricity $\epsilon_{\rm hydro} = \frac{\langle y^2-x^2\rangle}{\langle y^2+x^2\rangle}$, where averages are taken with respect to the number of participants in the transverse plane. The RHIC measurements (here by the STAR collaboration) are compared to the ideal hydrodynamic predictions. Figure from BaiThesis, presented in the review Teaney:2009qa.
• Figure 2: Comparison of the elliptic flow measured at RHIC (Au-Au collisions at $\sqrt{s}/A=200$GeV) and at the LHC (Pb-Pb collisions at $\sqrt{s}/A=2.76$TeV) Aamodt:2010pa.
• Figure 3: The elliptic flow predicted by viscous hydrodynamics, for different values of the shear viscosity per unit entropy $\eta/s$ and for Glauber (top) and color-glass condensate (bottom) initial conditions, compared to the measurements by the STAR collaboration at RHIC Luzum:2008cw.
• Figure 4: Concentration of sterile neutrinos produced in the early universe Asaka:2006nq. The dominant uncertainty comes from the limited knowledge of the spectral function.
• Figure 5: The 2+1 flavor QCD entropy density in units of $T^3$ as a function of temperature Borsanyi:2010cj.