Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian

Abstract

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 paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, 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.

invited review for Annual Reviews of Nuclear and Particle Science (2012); 21 pp., 4 tables, 6 figures. v2: Figures 2 and 5 updated; references added; many minor wording changes and clarifications; conforms closely to accepted version

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• Improved predictions for $\mu \to e$ conversion in nuclei and Higgs-induced lepton flavor violation
• Introduction to Big Bang Nucleosynthesis and Modern Cosmology
• Binary neutron star mergers as a probe of quark-hadron crossover equations of state
• Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits
• Lattice QCD Calculation of the Pion Mass Splitting
• Oklo reactors and implications for nuclear science
• Probing hadronization with flavor correlations of leading particles in jets
• The QCD Running Coupling and its Measurement
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Lattice regularisation and entanglement structure of the Gross-Neveu model
• Ken Wilson: Solving the Strong Interactions
• Effective scalar four-fermion interaction for Ge-phobic exothermic dark matter and the CDMS-II Silicon excess
• Critical exponents and transport properties near the QCD critical endpoint from the statistical bootstrap model
• Equation of state for hyperonic neutron-star matter in SU(3) flavor symmetry
• Neutron Star Mergers and the Quark Matter Equation of State
• Review of Neutral Naturalness
• Quark Flavor Physics Review
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• 't Hooft model in the temporal gauge