Membranes for topological M-theory

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) Spin(7). 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 r (o) over cap le of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.