TY - RPRT
T1 - Computing Amplitudes in topological M-theory
Y1 - 2007
A1 - Giulio Bonelli
A1 - Alessandro Tanzini
A1 - Maxim Zabzine
AB - We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ 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 $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.
JF - JHEP 03 (2007) 023
UR - http://hdl.handle.net/1963/1901
U1 - 2335
U2 - Mathematics
U3 - Mathematical Physics
ER -