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

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 Ans\"atze 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.