On confinement and duality

Confinement in four-dimensional gauge theories is considered from several points of view. General features are discussed, and the mechanism of confinement is investigated. Dualities between field theories, and duality between field theory and string theory, are both put to use. In these lectures I have given an overview of some of the key ideas underlying confinement as a property of field theory, and now, of string theory as well. This is a tiny fraction of what field theory (and now string theory) is capable of, and we are still uncovering new features on a monthly basis. In fact, most field theories do not have confinement, for reasons entirely different from those of QCD. Many become nontrivial conformal field theories at low energy. Others become composite, weakly-coupled gauge theories. Dualities of many stripes are found everywhere. Ordinary dimensional analysis in string theory is totally wrong in the regime where it looks like weakly-coupled field theory, and ordinary dimensional analysis in field theory is totally wrong in the regime where it looks like weakly-coupled supergravity