Four-dimensional spacetime physics from orbifold M-theory

By compactifying M-theory on S 1/ Z2 x T6/ Z7 orbifolds, we construct models containing the Standard Model of particle physics in four-dimensional spacetime. In such models, copies of the four-dimensional Worlds appear as sub-planes within the ten-dimensional planes, parallel to each other and connected by the 11th dimension. The E8 gauge symmetry on either ten-plane breaks down to some subgroup under the action of Z7 and produces the corresponding gauge fields and a matter spectrum in the four-plane. We have constructed a procedure to find Z7 invariant subgroups of E8, which is applicable to any ZN orbifold that preserves supersymmetry. All the models obtained in this way are either intrinsically anomalous or free of chiral fermions.; We find a relationship between our M-theory models and those constructed from compactifying E8 x E8 string theory on the same T 6/ Z7 orbifold. This provides conditions used to detect additional twisted states, which can cancel the anomalies and provide some chiral states. Some of the states relate the two four-dimensional Worlds through the five-planes present in our models.; We illustrate the calculation of the charges for these matter fields and find the anomalous U(1) factor that satisfy a universal Green-Schwarz (GS) relation. In the presence of gauge background fields, the Z7 -invariant gauge groups on a four-plane reduce to a smaller one and approach that in the Standard Model. We use Dynkin diagrams to showcase a model with SU(3) x SU(2) x U(1)5 gauge symmetry. And finally we discuss how to implement our ideas on higher order orbifolds.