Static correlation lengths in QCD at high temperature and finite densities

A brief review is given of the sign problem in finite density lattice QCD and various attempts to overcome it. To date there is still no solution to this problem which would work for realistic QCD. The main focus then is on the deconfined phase, where QCD can be described by a dimensionally reduced effective action. After summarizing derivation and validity of the effective theory, it is demonstrated that it can be simulated efficiently in the presence of a chemical potential for quarks $\mu/T\lsim 4$. Direct comparison of simulations with imaginary and real $\mu$ suggests that equilibrium plasma properties could be analytically continued from 4d QCD simulations at imaginary $\mu$.