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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 (QGP) using fully dressed selfconsistent 1- and 2-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, $(4π)η/s$, and the heavy-quark diffusion coefficient, $(2πT) {\cal D}_s$, 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 $ (4πη/s)/(2πT {\cal D}_s )$ as a measure to distinguish the perturbative and strong-coupling limits of 5/2 and 1, respectively.