Supersymmetry, G-flux and Spin(7) manifolds
  In this note we study warped compactifications of M-theory on manifolds of Spin(7) holonomy in the presence of background 4-form flux. The explicit form of the superpotential can be given in terms of the self -dual Cayley calibration on the Spin(7) manifold, in agreement with the general formula propsed in hep-th/9911011. 
Bobby Acharya, Sergei Gukov and Xenia de la Ossa