Superpotentials forM-theory on aG2holonomy manifold and triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on ${\bfS^3}\x {\bf S^3}$ we consider the superpotential generated by membraneinstantons and study its transformations properties, especially under monodromytransformations and triality symmetry. We find that the latter symmetry is,essentially, even a symmetry of the superpotential. As in Seiberg/Wittentheory, where a flat bundle given by the periods of an universal elliptic curveover the $u$-plane occurs, here a flat bundle related to the Heisenberg groupappears and the relevant universal object over the moduli space is related tohyperbolic geometry.Comment: 58 pages, latex; references adde