Supersymmetric QCD Sheds Light on Quark Confinement and the Topology of 4‐Manifolds

MAR 01, 1995

A new analytic computational technique has been developed in a wide class of supersymmetric Yang‐Mills models. In physics the technique provides some of the first general exact results in four‐dimensional quantum field theory, including a quantitative description of confinement via magnetic monopole condensation. In mathematics the topological study of smooth four‐dimensional manifolds has been revolutionized.

DOI: 10.1063/1.2807935

Graham P. Collins

Perturbation theory has long been one of the most successful tools in quantum field theory. The technique produces a series of terms, and ideally most of the “physics” is captured by the more readily computed early teims in the expansion, with later terms supplying progressively more negligible corrections. In contrast to such approximations, exact computations in four‐dimensional quantum field theory have been few and far between. As Stephen Shenker (Rutgers University) puts it, “The conventional wisdom was that exact results in four‐dimensional quantum field theory were essentially unobtainable.” This lack of analytic results has been particularly problematic for the theory of quark confinement, which involves the strong force in a thoroughly nonperturbative regime.