Massive String Theories From M-Theory and F-Theory

The massive IIA string theory whose low energy limit is the massive supergravity theory constructed by Romans is obtained from M-theory compactified on a 2-torus bundle over a circle in a limit in which the volume of the bundle shrinks to zero. The massive string theories in 9-dimensions given by Scherk-Schwarz reduction of IIB string theory are interpreted as F-theory compactified on 2-torus bundles over a circle. The M-theory solution that gives rise to the D8-brane of the massive IIA theory is identified. Generalisations of Scherk-Schwarz reduction are discussed.