Open Access
April 2006 On topological $M$-theory
Giulio Bonelli, Alessandro Tanzini, Maxim Zabzine
Adv. Theor. Math. Phys. 10(2): 239-260 (April 2006).


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.


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Giulio Bonelli. Alessandro Tanzini. Maxim Zabzine. "On topological $M$-theory." Adv. Theor. Math. Phys. 10 (2) 239 - 260, April 2006.


Published: April 2006
First available in Project Euclid: 30 July 2006

zbMATH: 1129.81064
MathSciNet: MR2249572

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 2 • April 2006
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