http://arxiv.org/abs/1506.08067 Braids as a representation space of SU(5) Daniel Cartin
(Submitted on 23 Jun 2015)
The Standard Model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary, is still unknown. Along the lines of previous preon models positing a substructure to explain these aspects, Bilson-Thompson showed how the first family of elementary particles is realized as the crossings of braids made of three strands, with charges resulting from twists of those strands with certain conditions; in this topological model, there are only two distinct neutrino states. Modeling the particles as braids implies these braids must be the representation space of a Lie algebra, giving the symmetries of the Standard Model. In this paper, this representation is made explicit, obtaining the raising operators associated with the Lie algebra of SU(5), one of the earliest grand unified theories. Because the braids form a group, the action of these operators are braids themselves, leading to their identification as gauge bosons. Possible choices for the other two families are also given. Although this realization of particles as braids is lacking a dynamical framework, it is very suggestive, especially when considered as a natural method of adding matter to loop quantum gravity.
9 pages, 7 figures

This is the first paper for a while on this topic (which I think goes to show that just because there hasn't been recent activity on some subject, that does not necessarily mean that the idea has been abandoned!). For example - I'm still waiting for Thiemann's paper on the "the LQG string" in curved space-time!

What this thread needs is:

A review of earlier papers/talks would be appropriate - stuff on the motivation from "noiseless sub-systems", the requirement that this applies to q-deformed (i.e. non-zero cosmological constant) versions of LQG (cus that is why you get one-dimensional links replaced by these ribbons that can have twists in them), dynamical rules that incorporate micro-causality as part of the substitution rules (I think?). The idea that these rules identify stable states which then make "interactions" as something that somehow violate these stables states (I think?).

Oh and a particle physicist to give us a primer on SU(5) as a GUT (SU(5) group containing SU(3) X SU(2) x U(1) as a sub-group), together with an explanation of the problem of non-observed proton decay.

With SU(5) you get proton decay which has not yet been observed experimentally, and the resulting lower limit on the lifetime of the proton contradicts the predictions of this model. However, the elegance of the model has led particle physicists to use it as the foundation for more complex models which yield longer proton lifetimes.

Is SO(10) one of these more complex models? A note:

"Historical note: Georgi found the SO(10) theory a few hours before finding SU(5) at the end of 1973". Apparently.

However, the mechanism by which you have `preon configurations' in q-deformed LQG is very different from "normal" particle physics - so you should not give up hope that somehow the q-deformed LQG approach may have resolutions to the non-observed proton decay that have yet to be understood! I think this is something they mention in the paper...along with other hopes of unforeseen constraining rules that could resolve other issues.

julian if they could show how even 1 lqg, braded ribbon in q-deformed can give rise to a SM particle like neutrino or photon with all properties, i'll be amazed. perhaps string theory can help here.

i.e you have 1 braided ribbon structure in LQG. you have an elementary particle like an electron. how do you show these ribbon structures have the properties of an electron?

perhaps if it can be shown these braided ribbon structures have string-like properties with worldsheets, then that could be an approach to SM

it would be interesting to speculate what would be the hypothetical properties of a fundamental object that (1) satisfies the ribbons he proposed and (2) gives rise to elementary particles of the SM.