Instanton induced compactification and fermion chirality

The question of fermion chirality in Kaluza-Klein theories with coupling to Yang-Mills fields is discussed. The argument is illustrated in eight dimensions where an SU(2) Yang-Mills field assumes the one-instanton form on the internal space. This serves not only to trigger spontaneous compactification of the internal space but will ensure the emergence of nl - nR = 3/3t(t + 1)(2t +1) zero modes in an irreducible eight-spinor belonging to the (2t + 1)-dimensional representation of SU(2)