In theoretical physics, the electroweak model breaks parity maximally. All its fermions are chiral Weyl fermions, which means that the charged weak gauge bosons W and W only couple to left-handed quarks and leptons.
Some theorists found this objectionable, and so conjectured a GUT extension of the weak force which has new, high energy W′ and Z′ bosons, which do couple with right handed quarks and leptons:
to
Here,  (pronounced " left") is  from above, while  is the baryon number minus the lepton number. The electric charge formula in this model is given by
where  and  are the left and right weak isospin values of the fields in the theory.
There is also the chromodynamic . The idea was to restore parity by introducing a left-right symmetry. This is a group extension of  (the left-right symmetry) by
to the semidirect product
This has two connected components where  acts as an automorphism, which is the composition of an involutive outer automorphism of  with the interchange of the left and right copies of  with the reversal of . It was shown by Mohapatra & Senjanovic (1975) that left-right symmetry can be spontaneously broken to give a chiral low energy theory, which is the Standard Model of Glashow, Weinberg, and Salam, and also connects the small observed neutrino masses to the breaking of left-right symmetry via the seesaw mechanism.
In this setting, the chiral quarks
and
are unified into an irreducible representation ("irrep")
The leptons are also unified into an irreducible representation
The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model are
This then provides three sterile neutrinos which are perfectly consistent with  neutrino oscillation data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.
Because the left–right symmetry is spontaneously broken, left–right models predict domain walls. This left-right symmetry idea first appeared in the Pati–Salam model (1974) and Mohapatra–Pati models (1975).