We examine the compactification of D=4+2N, Einstein-Maxwell-Dirac theory. It is shown that the manifold CPN × M4 is a solution of the equations of motion. The structure of the fermions, gauge bosons and their couplings in the four-dimensional effective theory is investigated. The scale of CPN is quantized by a generalized Dirac condition. When the results are applied to the solution with internal space CP1×CP2, the weak mixing angle and the ratio of the couplings of SU(3) (g3) and SU(2) (g2) are defined by two integers and a hypercharge. An SU(3)-triplet chiral fermion can appear in four-dimensional effective theory.
ASJC Scopus subject areas
- Nuclear and High Energy Physics