The Incredible Shrinking Torus

TL;DR

This paper explores the dualities of M-theory compactified on tori using super Yang-Mills theories, revealing remarkable symmetries, unusual dynamics, and the emergence of extra dimensions in certain limits.

Contribution

It provides new insights into the behavior of super Yang-Mills theories under toroidal compactifications, including the emergence of an extra spatial dimension.

Findings

Dualities lead to conjectured symmetries and relations.

Studying small tori reveals strongly coupled fixed points.

Emergence of an additional spatial dimension in four-torus compactification.

Abstract

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.