THE INCREDIBLE SHRINKING TORUS

Using M(atrix) theory, the dualities of toroidally compactified M-theo ry can be formulated as properties of super Yang Mills theories in var ious dimensions. We consider the cases of compactification on 1-, 2-, 3-, 4- and 5-dimensional tori. The dualities required by string theory lead to conjectures of remarkable symmetries and relations between fi eld theories as well as extremely unusual dynamical properties. By stu dying the theories in the limit of vanishingly small tori, a wealth of information is obtained about strongly coupled fixed points of super Yang-Mills theory in various dimensions. Perhaps the most striking beh avior, as noted by Rozali in this context, is the emergence of an addi tional dimension of space in the case of a 4-torus. (C) 1997 Elsevier Science B.V.