The renormalization group plays an essential role in many areas of physics, both
conceptually and as a practical tool to determine the long-distance low-energy properties of …

We discuss our present knowledge of α s, the fundamental running coupling or effective
charge of Quantum Chromodynamics (QCD). A precise understanding of the running of α s …

We discuss the phase structure of QCD for N f= 2 and N f= 2+ 1 dynamical quark flavors at
finite temperature and baryon chemical potential. It emerges dynamically from the …

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field
theories, in particular for quantum gravity. Significant progress on this program has led to a …

We review results for the phase diagram of QCD, the properties of quarks and gluons and
the resulting properties of strongly interacting matter at finite temperature and chemical …

Recent experimental developments in diverse areas—ranging from cold atomic gases to
light-driven semiconductors to microcavity arrays—move systems into the focus which are …

Asymptotic safety generalizes asymptotic freedom and could contribute to understanding
physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet …

This book covers recent developments in the covariant formulation of quantum gravity.
Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to …

For decades, frustrated quantum magnets have been a seed for scientific progress and
innovation in condensed matter. As much as the numerical tools for low-dimensional …

The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are
crucial for the internal consistency of the theory; most notably, they account for the …