Membranes for Topological M-Theory

Abstract

We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.

22 pp, plain tex. v2: refs. added

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Cited by in corpus (9)

• Open G2 Strings
• On the refined counting of graphs on surfaces
• Membranes for Topological M-Theory
• A Note on Topological M5-branes and String-Fivebrane Duality
• AKSZ constructions for topological membranes on $G_2$-manifolds
• G2 Hitchin functionals at one loop
• Computing Amplitudes in topological M-theory
• On topological M-theory
• The B-model on the A-model NS5-brane