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Chirality and BSM

Posted by Sparticles under

BSM,

Field Theory
[2] Comments
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?

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December 3, 2008 at 3:04 am

some comments on chirality. most people know that in string theory typeIIB is chiral and typeIIA is non chiral. the question is that if this fact affects in the attempts on compactification down to 4d or 5d(for RS people). since the chirality in the ten dimensional theory are on gravitinos (2 gravitinos means N=2 susy for example). We always try to get to N=1 susy during the compactification (in type IIB people try orientifolds to get rid of half of the supersymmetries). Then both type IIA and type IIB will have one gravitino left after compactification. so it seems to me that people always pay attention to type IIB doesn’t have to do with the fact that it’s chiral.

some further comments:

1 type IIA and type IIB are T-dual to each other after changing the compactification circle size. so why should we only be able to get standard model(for example) from one but not the other

2 type IIB is more popular because complex structure moduli space belongs to vector multiplet (I simply remember this sentence to attempt future understanding) and it’s easier to study. But is this related to the chirality of type IIB? I dont’ know.

December 10, 2008 at 7:52 am

[…] the most sensible representation because the Standard Model is a chiral theory. (We’ve got a previous post on this point, too.) Thus working with the two-component fermions give a better handle for the […]