Possible Gauge Theoretic Origin for Quark-Lepton Complementarity

The experimentally observed relation between the solar mixing angle $\theta_{\odot}$ and the Cabibbo angle $\theta_c$ i.e. $\theta_{\odot}+\theta_c = \pi/4$ has been conjectured to be a possible indication for quark lepton unification at high scales. In this letter, we present a gauge model based on $SU(2)_L \times SU(2)_R\times SU(4)_c$ that lead to this relation using the double seesaw formula for neutrino mass. The model predicts an inverted mass hierarchy for neutrinos. The original gauge symmetry breaks down at the multi-TeV scale and can therefore lead to observable effects in low energy leptonic processes. We also discuss a possible gauge model based on an $E_6$ inspired trinification $SU(3)_C \times SU(3)_L \times SU(3)_R$ model, more closely allied to string theory by the AdS/CFT correspondence.