Classification and Moduli Kahler Potentials of G_2 Manifolds
  Compact manifolds of G_2 holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kahler potential for M-theory on the resulting class of G_2 manifolds with blown up co-dimension four singularities. 
Adam B Barrett and Andre Lukas