Physics – High Energy Physics – High Energy Physics - Theory

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2006-11-29

JHEP 0703:023,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

10.1088/1126-6708/2007/03/023

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.

**Bonelli Giulio**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Tanzini Alessandro**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Zabzine Maxim**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

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