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arXiv · hep-th/0611327

Computing Amplitudes in topological M-theory

Giulio Bonelli·Alessandro Tanzini·Maxim Zabzine
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Abstract

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. In 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.

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Giulio Bonelli, Alessandro Tanzini, Maxim Zabzine. 2007-03-06. Computing Amplitudes in topological M-theory. https://doi.org/10.1088/1126-6708%2F2007%2F03%2F023

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