progress in the understanding of the dynamics of supersymmetric theories (for recent reviews and an extensive list of references see ) uncovered the crucial role played by electric-magnetic duality \[\] in understanding the strong coupling dynamics. In scale invariant theories like the $N=4$ \[\] and finite $N=2$ theories \[\] duality provides two different descriptions of the same physical system that are equivalent at all distance scales. In asymptotically free theories the underlying degrees of freedom are visible at short distance and therefore the existence of different descriptions that are equivalent at all scales (exact duality) is impossible. Nevertheless, duality may be generalized to such theories \[\], relating different quantum field theories with the same long distance behavior. When this long distance behavior is described by a non-trivial superconformal quantum field theory the dual theories are in the same universality class – they flow to the same fixed point of the renormalization group. When one of these theories is infra-red free it gives a simple description of the long distance physics of its strongly coupled dual.

No proof of this duality is known but there is a lot of evidence supporting it. There are three kinds of independent tests:

[1.]{} The 