Twenty-First Century Lattice Gauge Theory: Results from the Quantum Chromodynamics Lagrangian

Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to a simple nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true without having been demonstrated to be true. This article reviews various results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This research sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, and other intriguing features such as the phase structure of QCD. Also, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.