Towards gauge coupling unification in left-right symmetric SU (3) c ×sU (3) L ×sU (3) R× U (1) X theories

We consider the possibility of gauge coupling unification within the simplest realizations of the SU(3)c×SU(3)L×SU(3)R×U(1)X gauge theory. We present a first exploration of the renormalization group equations governing the "bottom-up" evolution of the gauge couplings in a generic model with free normalization for the generators. Interestingly, we find that for a SU(3)c×SU(3)L×SU(3)R×U(1)X symmetry breaking scale MX as low as a few TeV one can achieve unification in the presence of leptonic octets. We briefly comment on possible grand unified theory frameworks which can embed the SU(3)c×SU(3)L×SU(3)R×U(1)X model as well as possible implications, such as lepton flavor violating physics at the LHC.