Spectral and transport properties of quark–gluon plasma in a nonperturbative approach

Nonperturbative methods play an important role in quantum many-body systems, especially in situations with an interplay of continuum and bound states and/or large coupling strengths between the constituents. Employing the Luttinger–Ward functional (LWF) we have computed the equation of state (EoS) of the quark–gluon plasma using fully dressed selfconsistent one- and two-body propagators. We first give an alternative derivation of our previously reported results for resumming the ladder diagram series of the LWF using a “matrix log” technique which accounts for dynamically formed bound and resonant states. Two types of solutions were found in selfconsistent fits to lattice-QCD data for the EoS, heavy-quark free energy and quarkonium correlators: a strongly coupled scenario (SCS) with broad parton spectral functions and strong meson resonances near the transition temperature vs. a weakly coupled scenario (WCS) with well-defined parton quasiparticles and weak meson resonances. Here, we discuss how these solutions can be distinguished by analyzing the pertinent transport properties. We focus on the specific shear viscosity, ( 4 π ) η / s , and the heavy-quark diffusion coefficient, ( 2 π T ) D s , including its mass dependence. At low temperatures, in the SCS, they turn out to be a factor of 2 within their conjectured quantum lower bound, while they are a factor of 2–5 larger in the WCS. At higher temperatures, the transport parameters of the two scenarios approach each other. We propose the ratio ( 4 π η / s ) / ( 2 π T D s ) as a measure to distinguish the perturbative and strong-coupling limits of 5/2 and 1, respectively.