Messages for QCD from the Superworld

Recent discoveries in supersymmetric gauge theories have significant implications for our understanding for QCD and of field theory in general. The phases of N=1 supersymmetric QCD (SQCD) are discussed, and the possibility of similar phases in non-supersymmetric QCD is emphasized. It is described how duality in SQCD links many previously known duality transformations that were thought to be distinct, including Olive-Montonen duality of N=4 supersymmetric gauge theory and quark-hadron duality in (S)QCD. A link between Olive-Montonen duality and the confining strings of (S)QCD is explained, in which a picture of confinement via non-abelian monopole condensation --- a generalized dual Meissner effect --- emerges explicitly. In this picture, unlike previous ones, the confining flux tubes carry the correct Z_N discrete charges. A number of studies of these subjects, which could be carried out using lattice gauge theory, are proposed.Comment: Talk given at YKIS '97, Kyoto, Japan. 24 pages, 3 figures, uses ptptex.sty,ptpprep.st

Manifolds of Fixed Points and Duality in Supersymmetric Gauge Theories

There are many physically interesting superconformal gauge theories in four dimensions. In this talk I discuss a common phenomenon in these theories: the existence of continuous families of infrared fixed points. Well-known examples include finite ${\cal N}=4$ and ${\cal N}=2$ supersymmetric theories; many finite ${\cal N}=1$ examples are known also. These theories are a subset of a much larger class, whose existence can easily be established and understood using the algebraic methods explained here. A relation between the ${\cal N}=1$ duality of Seiberg and duality in finite ${\cal N}=2$ theories is found using this approach, giving further evidence for the former. This talk is based on work with Robert Leigh (hep-th/9503121).Comment: Talk given at YKIS'95; 15 pp., uses ReVTeX, 3 uuencoded figure

Confining Phase of Three Dimensional Supersymmetric Quantum Electrodynamics

Abelian theories in three dimensions can have linearly confining phases as a result of monopole-instantons, as shown, for SU(2) Yang-Mills theory broken to its abelian subgroup, by Polyakov. In this article the generalization of this phase for N=2 supersymmetric abelian theories is identified, using a dual description. Topologically stable BPS-saturated and unsaturated particle and string solitons play essential roles. A plasma of chiral monopoles of charge 1 and -1 (along with their antichiral conjugates) are required for a stable confining vacuum. N=2 SU(2) Yang-Mills theory broken to U(1) lacks this phase because its chiral monopoles all have the same charge, leading to a runaway instability. The possibility of analogous confining phases of string theory, and a dual field theoretic model thereof, are briefly discussed.Comment: 18 pages, 8 figures, uses sprocl.tex. Submitted as a contribution to the Yuri Golfand memorial volum