Computing Amplitudes in topological M-theory
arXiv:hep-th/0611327 · doi:10.1088/1126-6708/2007/03/023
Abstract
We define a topological quantum membrane theory on a seven dimensional manifold of holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. In particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the , we find that the amplitudes of our model are related to Joyce invariants.
26 pages