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)×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.