The membrane instanton superpotential for M-theory on the G 2 holonomy manifold given by the cone on S 3 × S 3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dil...

In this paper, we obtain a new common fixed point theorem by using a new contractive condition in cone metric spaces. Our result generalizes and extends well known result in complete metric spaces.

Let Ξ(H) denote the set of all nonzero closed convex cones in a finite dimensional Hilbert space H. Consider this set equipped with the bounded Pompeiu-Hausdorff metric δ. The collection of all pointed cones forms an open set in the metric space (Ξ(H), δ). One possible way of measuring the degree of pointedness of a cone K is by evaluating the distance from K to the set of all nonpointed cones....