Dimensional reduction of exceptional E₆, E₈ gauge groups and flavour chirality

Ten-dimensional Yang-Mills gauge theories based on the exceptional groups E₆ and E₈ are reduced to four-dimensional flavour-chiral Yang-Mills-Higgs theories where the extra six dimensions are identified with the compact G₂/SU(3) and SO(7)/SO(6) coset spaces. A ten-dimensional E₈ theory leads to three families of SU(5), one of which lies in the 144-dimensional representation of SO(10).