Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD

Abstract

A discussion on the electrical conductivity of the quark-gluon plasma as determined by lattice QCD is given. After a reminder of basic definitions and expectations, various methods for spectral reconstruction are reviewed, including the use of Ansätze and sum rules, the Maximum Entropy and Backus-Gilbert methods, and Tikhonov regularisation. A comprehensive overview of lattice QCD results obtained so far is given, including a comparison of the different lattice formulations. A noticeable consistency for the conductivities obtained is seen, in spite of the differences in the lattice setups and spectral reconstruction methods. It is found that in the case of quenched QCD little temperature dependence of $\sigma /T$ is seen in the temperature range investigated, while for QCD with dynamical quarks a reduction of $\sigma /T$ in the vicinity of the thermal crossover is observed, compared to its value in the QGP. Several open questions are posed at the end.

arXiv comment13 pages, 3 figures, invited contribution to the EPJA topical issue "Theory of hot matter and relativistic heavy-ion collisions (THOR)"

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• Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions
• Conductivity, diffusivity, and violation of Wiedemann-Franz Law in a hadron resonance gas with van der Waals interactions
• Direct photons emission rate and electric conductivity in twice anisotropic QGP holographic model with first-order phase transition
• Charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics
• Spin polarization dynamics in the Bjorken-expanding resistive MHD background
• Static magnetic susceptibility in finite-density SU(2) lattice gauge theory
• Spectral and transport properties from lattice QCD
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• Lattice QCD noise reduction for bosonic correlators through blocking
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• Directed flow of D and B mesons in an electrically and chirally conductive QGP at LHC energies
• QCD at high temperature and density: selected highlights