Leptons in Holographic Composite Higgs Models with Non-Abelian Discrete Symmetries

We study leptons in holographic composite Higgs models, namely in models possibly admitting a weakly coupled description in terms of five-dimensional (5D) theories. We introduce two scenarios leading to Majorana or Dirac neutrinos, based on the non-abelian discrete group $S_4\times \Z_3$ which is responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino masses is naturally explained and normal/inverted mass ordering can be accommodated. We analyze two specific 5D gauge-Higgs unification models in warped space as concrete examples of our framework. Both models pass the current bounds on Lepton Flavour Violation (LFV) processes. We pay special attention to the effect of so called boundary kinetic terms that are the dominant source of LFV. The model with Majorana neutrinos is compatible with a Kaluza-Klein vector mass scale $m_{KK}\gtrsim 3.5$ TeV, which is roughly the lowest scale allowed by electroweak considerations. The model with Dirac neutrinos, although not considerably constrained by LFV processes and data on lepton mixing, suffers from a too large deviation of the neutrino coupling to the $Z$ boson from its Standard Model value, pushing $m_{KK}\gtrsim 10$ TeV.