New potentials from Scherk-Schwarz reductions

Abstract

We study compactifications of eleven-dimensional supergravity on Calabi-Yau threefolds times a circle, with a duality twist along the circle a la Scherk-Schwarz. This leads to four-dimensional {N} = 2 gauged supergravity with a semi-positive definite potential for the scalar fields, which we derive explicitly. Furthermore, inspired by the orientifold projection in string theory, we define a truncation to {N} = 1 supergravity. We determine the D-terms, Kähler-and superpotentials for these models and study the properties of the vacua. Finally, we point out a relation to M-theory compactifications on seven-dimensional manifolds with G 2 structure.