Supersymmetry and Strongly Coupled Gauge Theories

Unlike many of the other talks at this symposium, this one will not take supersymmetry “seriously”: instead of being concerned with how or if supersymmetry enters physics beyond the Standard Model, this talk will treat supersymmetry merely as a technical tool to shed light on the strong coupling behavior of gauge field theories in general. Supersymmetric field theories are especially simple and symmetrical field theories, and as such are particularly “well behaved”. We study the unusual or singular behavior of supersymmetric theories with the expectation that whatever can happen in a supersymmetric vacuum, will happen in spades in non-supersymmetric theories. In the first part of this talk I will briefly outline those features special to supersymmetric theories which together provide a powerful handle on the nonperturbative vacuum structure of these theories. The second part will then describe some of the more unusual or unexpected things we have learned about strongly coupled gauge theories. This discussion will be formulated in the guise of three open questions. Here I restrict myself to Lorentz invariant gauge field theories without gravity in 4, 5, and 6 dimensions with 8 or 16 hermitian conserved supercharges. These restrictions are just to keep this talk short: field theories in lower dimensions and with fewer supersymmetries have an even greater variety of strong coupling behaviors, and likewise for gravitational (i.e. string) theories.