Flavor Non-universal Pati-Salam Unification and Neutrino Masses

We analyze the neutrino mass spectrum and discuss the extra-dimensional interpretation of a three-site Pati-Salam model which i) unifies all families of quark and leptons, ii) provides a natural description of the Standard Model Yukawa couplings, iii) could account for the recent $B$-physics anomalies. The key feature of the model is a breaking of the Pati-Salam and electroweak gauge symmetries localized on opposite sites, communicated to the other sites in an attenuated manner via nearest-neighbor interactions. We show that in this context gauge-singlet fermions localized on each site, receiving hierarchical Majorana masses, can allow the implementation of an inverse seesaw mechanism leading to light anarchic neutrino masses consistent with data. The continuum limit of this three-site setup has a natural interpretation in terms of a warped extra dimension with three defects, where the required exponential hierarchies can be achieved from $\mathcal{O}(1)$ differences in the bulk field masses.