The QCD phase diagram

Strongly interacting matter exhibits new phases under extreme conditions. Matter was exposed to such extremes not only in the Early Universe, but also today in the cores of neutron stars, as well as in laboratory experiments at a much smaller scale. We study the underlying theory, Quantum Chromodynamics (QCD) with the methods of statistical physics and explore the various phases we may encounter in experiment, such as the Quark Gluon Plasma. We briefly summarize the experimental evidence for the new forms of matter and review the theoretical efforts to embed these findings in the broader context of quantum field theory, with special attention to exact and broken symmetries and critical behaviour.