  We analyze a scenario where the right-handed neutrinos make part of a
strongly coupled conformal field theory and acquire an anomalous dimension
\gamma<1 at a large scale \Lambda. Their Yukawa couplings to the Higgs become
irrelevant at the fixed point and they are suppressed at low scales giving rise
naturally to a small (sub-meV) Dirac neutrino mass which breaks the conformal
invariance. We derive an upper bound on \gamma from loop-induced flavor
changing neutral currents. Neutrino Yukawa couplings can be sizable at
electroweak scales and therefore the invisible decay of the Higgs in the
neutrino channel can be comparable to the c\bar c and \tau\bar\tau modes and
predict interesting Higgs phenomenology. If lepton number is violated in the
conformal theory an irrelevant Majorana mass operator for right-handed
neutrinos appears for \gamma>1/2 giving rise to an inverse see-saw mechanism.
In this case light sterile neutrinos do appear and neutrino oscillation
experiments are able to probe our model.
