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Bonelli, Giulio; Tanzini, Alessandro; Zabzine, Maxim

On topological M-theory. (English) Zbl 1129.81064

Adv. Theor. Math. Phys. 10, No. 2, 239-260 (2006).
Summary: 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 \(M\times S^1\), 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.

Cited in 3 Documents

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T45 Topological field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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\textit{G. Bonelli} et al., Adv. Theor. Math. Phys. 10, No. 2, 239--260 (2006; Zbl 1129.81064)
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