Flipped SO(10)


Flipped SO is a Grand Unified Theory which is to standard SO(10) as flipped SU(5) is to SU(5).

Details

In conventional SO models, the fermions lie in three spinorial 16 representations, one for each generation, which decomposes under /Z5 as
This can either be the Georgi–Glashow SU or flipped SU.
In flipped SO models, however, the gauge group is not just SO but SOF × UB or /Z4. The fermion fields are now three copies of
These contain the Standard Model fermions as well as additional vector fermions with GUT scale masses. If we suppose /Z5 is a subgroup of SOF, then we have the intermediate scale symmetry breaking /Z4 → /Z5 where
In that case,
note that the Standard Model fermion fields come from all three /Z4 representations. In particular, they happen to be the 101 of 161, the of 10−2 and the 15 of 14 × U notation with SU × U.
The other remaining fermions are vectorlike. To see this, note that with a 161H and a Higgs field, we can have VEVs which breaks the GUT group down to /Z5. The Yukawa coupling 161H 161 10−2 will pair up the 5−2 and fermions. And we can always introduce a sterile neutrino φ which is invariant under /Z4 and add the Yukawa coupling
OR we can add the nonrenormalizable term
Either way, the 10 component of the fermion 161 gets taken care of so that it is no longer chiral.
It has been left unspecified so far whether /Z5 is the Georgi–Glashow SU or the flipped SU. This is because both alternatives lead to reasonable GUT models.
One reason for studying flipped SO is because it can be derived from an E6 GUT model.