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On topological M-theory

Giulio Bonelli·Alessandro Tanzini·Maxim Zabzine
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Abstract

We construct a gauge fixed action for topological membranes on $G_2$-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on $M\times S^1$ the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on $G_2$-manifolds. We also generalize our construction to topological $p$--branes on special manifolds by exploring a relation between vector cross product structures and TFTs.

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Giulio Bonelli, Alessandro Tanzini, Maxim Zabzine. 2005-09-29. On topological M-theory. https://arxiv.org/abs/hep-th/0509175

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