  Using M(atrix) Theory, the dualities of toroidally compactified M-theory can
be formulated as properties of super Yang Mills theories in various dimensions.
We consider the cases of compactification on one, two, three, four and five
dimensional tori. The dualities required by string theory lead to conjectures
of remarkable symmetries and relations between field theories as well as
extremely unusual dynamical properties. By studying the theories in the limit
of vanishingly small tori, a wealth of information is obtained about strongly
coupled fixed points of super Yang-Mills theories in various dimensions.
Perhaps the most striking behavior, as noted by Rozali in this context, is the
emergence of an additional dimension of space in the case of a four torus.
