M-theory on Spin(7) manifolds, fluxes and 3D, N=1 supergravity

We calculate the most general causal N=1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using ectoplasmic integration theory. One example of such an action can be obtained by compactifying M-theory on a Spin(7) holonomy manifold taking non-vanishing fluxes into account. We show that the resulting three-dimensional theory is in agreement with the more general construction. The scalar potential resulting from Kaluza-Klein compactification stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. This potential can be written in terms of the superpotential previously discussed in the literature.