A 3d effective lattice theory for phase transitions in Yang-Mills and heavy dense QCD

QCD thermodynamics is crucial for the physics of the early universe, heavy ion collisions and compact stars. However, predictions by lattice simulations are very costly or, in the case of finite baryon density, even impossible because of a sign problem. Starting from Yang- Mills theory, I review how to use strong coupling methods to construct a 3d effective theory which reproduces the deconfinement phase transition to about 10% accuracy. The generalisation to QCD, which is valid for heavy quarks, has only a mild sign problem in the case of finite density and can be simulated efficiently. Moreover, it allows to address the nuclear liquid gas transition in the cold and dense regime for the first time directly from QCD. (paper)