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October 2006 Topological membrane theory from Mathai-Quillen formalism
Lilia Anguelova, Annamaria Sinkovics, Paul de Medeiros
Adv. Theor. Math. Phys. 10(5): 713-745 (October 2006).


It is suggested that topological membranes play a fundamental role in the recently proposed topological $M$-theory. We formulate a topological theory of membranes wrapping associative three-cycles in a sevendimensional target space with $G_2$ holonomy. The topological BRST rules and BRST invariant action are constructed via the Mathai–Quillen formalism. In a certain gauge, we show this theory to be equivalent to a membrane theory with two BRST charges found by Beasley and Witten. We argue that at the quantum level, an additional topological term should be included in the action, which measures the contributions of membrane instantons. We construct a set of local and non-local observables for the topological membrane theory. As the BRST cohomology of local operators turns out to be isomorphic to the de Rham cohomology of the $G_2$ manifold, our observables agree with the spectrum of $d = 4$, $N = 1 G_2$ compactifications of $M$-theory.


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Lilia Anguelova. Annamaria Sinkovics. Paul de Medeiros. "Topological membrane theory from Mathai-Quillen formalism." Adv. Theor. Math. Phys. 10 (5) 713 - 745, October 2006.


Published: October 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1115.81373
MathSciNet: MR2281546

Primary: 53Dxx
Secondary: 81T45

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 5 • October 2006
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