Quantum Chromodynamics (QCD) provides the fundamental description of the strong nuclear force and is a key component of the Standard Model of particle physics. The strong interactions are responsible, among other things, for binding protons and neutrons into nuclei, in spite of the electromagnetic repulsion of the protons. QCD is a quantum gauge field theory with local SU(3) symmetry that describes the interactions of colored quarks and gluons. They are observed to be “confined” inside the color-neutral hadronic states, such as the protons, neutrons and pi-mesons. The color confinement is among the most important and fascinating phenomena in fundamental physics. The celebrated asymptotic freedom of QCD implies that the gauge coupling vanishes in the short distance limit. The converse effect is its growth at long distances, giving rise to a host of non-perturbative phenomena including chiral symmetry breaking and the appearance of a mass gap related to the absence of the colored particles (quarks and gluons) as asymptotic states. While evidence for these phenomena has been provided by the numerical lattice simulations of QCD, as well as by simplified theoretical models, their proof in QCD is still missing. This is a profound problem, which is the first in the list of Clay Millennium Problems. One of the goals of the new Simons collaboration is to improve our understanding of confinement.
A characteristic feature of confinement is the formation of chromoelectric flux tubes, often called QCD strings, that can connect a quark with an antiquark. These strings have been observed in numerical lattice calculations, and they appear naturally in the description of certain confining gauge theories by higher-dimensional gravitational theories. The generalization of QCD from 3 to N colors, and the subsequent large N limit of gauge theories, offer a particularly good vantage point on the confining strings, since their splitting and joining becomes suppressed. As a result, a single flux tube becomes a consistent quantum system. In recent years, there has been significant progress towards understanding the dynamics of a long QCD string thanks to coordinated advances in analytical approaches and lattice simulations. More broadly, solving the large N QCD has been a long-standing dream of many theorists, towards which the Simons collaboration will devote renewed effort.
Several recent developments, ranging from fundamental theory, to numerical computation, to experimental discoveries, make this an opportune time to deepen our understanding of the non-perturbative aspects of QCD and other strongly interacting gauge theories. All the available methods will be employed in working on these important physics problems. This will help create a broader and more versatile community of researchers working on confinement and QCD strings.