G(2) Hitchin functionals at one loop

We consider the quantization of the effective target space description of topological M-theory in terms of the Hitchin functional whose critical points describe seven manifolds with a G(2) structure. The one-loop partition function for this theory is calculated and an extended version of it, that is related to the generalized G(2) geometry, is compared with the topological G(2) string. We relate the reduction of the effective action for the extended G(2) theory to the Hitchin functional description of the topological string in six dimensions. The dependence of the partition functions on the choice of background G(2) metric is also determined.