BPS-like potential for compactifications of heterotic M-theory?

We analyze the possibility to rewrite the action of Horava-Witten theory in a BPS-like form, which means that it is given as a sum of squares of the supersymmetry conditions. To this end we compactify the theory on a seven dimensional manifold of SU(3) structure and rewrite the scalar curvature of the compactification manifold in terms of the SU(3) structure forms. This shows that a BPS-like form cannot be obtained in general, but only for certain types of compactifications.