Orbifold and Orientifold Compactifications of F-Theory and M-Theory to   Six and Four Dimensions
  We study orbifold compactifications of F-theory which lead to $N=1$ supersymmetry in 6 and 4 spacetime dimensions. These are dual to specific orientifolds of M-theory, and in many cases to orientifolds of type IIB string theory. The equivalences are demonstrated by mapping the orbifolding transformations in the F, M and string theories to each other using dualities. We observe that M and F-theory appear to possess a property similar to discrete torsion in string theory. This is related to an ambiguity recently noted by Polchinski in the orientifold projection for 6-dimensional models. The 4-dimensional compactifications exhibit similar features, from which we predict the existence of certain new orientifolds of type IIB. Some orbifolds with higher supersymmetry are also examined. 
Rajesh Gopakumar (Princeton University), Sunil Mukhi (Tata Institute,   Mumbai)