We construct a gauge-fixed action for topological membranes on G 2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that the path integral in this gauge localizes on associative submanifolds. Moreover on M × 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.
On topological M theory / Bonelli, G.; Tanzini, A.; Zabzine, M.. - In: ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS. - ISSN 1095-0761. - 10:2(2006), pp. 239-260. [10.4310/ATMP.2006.v10.n2.a4]
On topological M theory
Bonelli, G.;Tanzini, A.;
2006-01-01
Abstract
We construct a gauge-fixed action for topological membranes on G 2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that the path integral in this gauge localizes on associative submanifolds. Moreover on M × 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.| File | Dimensione | Formato | |
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