About lepton number, I suspect that B-L is the Kaluza-Klein symmetry related to the 12th dimension, and given that it is beyond the maximum dimension of M-theory, I would prefer if the break down from 12 to 11 were of an different kind, unrelated to gauge bosons, when compared with the rest of the descent, from 11 to 4.

For framework, let’s suppose a theory something like d=4 N=8 supergravity arising from M-theory. The 84 degrees of freedom of the 3-form tensor are bosonic, so 84 protected fermionic degrees of freedom would need to be superpartners of the 3-form. But in fact, the 84 protected fermionic degrees of freedom are different for the two types of mass (though they have a large overlap). So we might suppose they are related to the 3-form by two different SUSY generators, perhaps an N=2 subalgebra of the full N=8 supersymmetry. This is my first observation.

Next I ask: what sort of «symmetry» prevents Majorana mass? Charge conservation! Since M2/M5 duality is an electric/magnetic duality, we might suppose that the two SUSY generators somehow relate to electric coupling of 3-form to M2-brane, and magnetic coupling of 3-form to M5-brane. The «electric superpartners» of the 3-form have no Majorana mass, the «magnetic superpartners» of the 3-form have no fundamental Dirac mass – that is a possible concept.

Finally we can ask how Dirac mass and Majorana mass are generated in string theory (if we want to take an «orthodox» approach to realizing this idea). The answer seems to be that they can be generated in many ways, but especially interesting might be «D-instantons», D-brane instantons (in the full theory they will be M-brane instantons). I didn’t find an obvious way to continue, but also no obvious refutation.

So summing up, one possible way to think about this idea is, that the M2/M5-brane duality of M-theory is responsible for the standard model mass spectrum, by way of an N=2 superalgebra applied to the supergravity 3-form. 🙂

But in the dual idea for neutrinos, we have 12 degrees of freedom are light and 84 degrees of freedom are «heavy». So it seems that here, the symmetry should be associated with the first group, the 12 degrees of freedmo?