Is it just me or does fermion chirality play a big role in beyond the standard model physics?
The Standard Model is a chiral theory; left- and right-handed fermions (i.e. -/+ eigenstates of the chirality operator ) live in different representations of the SM gauge group. This poses a rather rigid constraint on what kind of model becomes effective at the TeV scale.
Chirality prevents the use of low-scale models with multiple supersymmetries (), since this means one would be able to take a spin +1/2 fermion and expect to find a spin -1/2 fermion in the same supermultiplet (i.e. with the same gauge quantum numbers).
In extra dimensional models, the lack of a chiral operator in 5 dimensions (and more generally for most higher dimensions) stunted the development of KK models until the 80s. In a nutshell, there exists no chirality operator in five dimensions ( is just an ‘ordinary’ gamma matrix) and hence all fermions are Dirac rather than Weyl. This has led to lots of work with orbifolds and boundary conditions. [It might be neat to think about how such boundary conditions for different backgrounds could come from string theory.]
Even in lattice field theory, there is a “Nielsen Ninomiya No-Go” theorem for chiral fermions. (“No-Go Theorum for Regularizing Chiral Fermions [sic.]”)
I wonder if there are still novel ways to get chiral fermions from these theories that are just waiting for a clever model-builder to figure out?