A Note on Flux Induced Superpotentials in String Theory
  Non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped M-theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction. 
Melanie Becker and Dragos Constantin