M-theory potential from the G 2 Hitchin functional in superspace

We embed the component fields of eleven-dimensional supergravity into a superspace of the form x × y where x is the standard 4d, n = 1 superspace and y is a smooth 7-manifold. the eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of y . it contains a natural candidate for a g 2 structure on y , and being a complex of superforms, defines a superspace chern-simons invariant. adding to this a natural generalization of the riemannian volume on x × y and freezing the (superspin- $$ {scriptscriptstyle frac{3}{2}} $$ and 1) supergravity fields on x, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. in this approximation the action is the sum of the superspace chern-simons term and a super-space generalization of the hitchin functional for y as a g 2-structure manifold. integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. the latter reproduces the einstein-hilbert term on y in a form due to bryant.