Unification of elementary forces in gauge SL(2N,C) theories

Abstract: We argue that the gauge $SL(2N,C)$ theories may point to a possible way where the known elementary forces, including gravity, could be consistently unified. Remarkably, while all related gauge fields are presented in the same adjoint multiplet of the $SL(2N,C)$ symmetry group, the tensor field submultiplet providing gravity can be naturally suppressed in the weak-field approach developed for accompanying tetrad fields. As a result, the whole theory turns out to effectively possess the local $SL(2,C)\times SU(N)$ symmetry so as to naturally lead to the $SL(2,C)$ gauge gravity, on the one hand, and the $SU(N)$ grand unified theory, on the other. Since all states involved in the $SL(2N,C)$ theories are additionally classified according to their spin values, many possible $SU(N)$ GUTs - including the conventional one-family $SU(5)$ theory - appear not to be relevant for the standard $1/2$ spin quarks and leptons. Meanwhile, the $SU(8)$ grand unification for all three families of composite quarks and leptons that stems from the $SL(16,C)$ theory seems to be of special interest that is studied in some detail.