Yidun Wan gave a very nice talk a week or so ago at Perimeter. It is on video http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=7a27faa9-6d55-41fb-9fba-6901167c2bb5&shouldResize=False [Broken] This is part of a research effort by a handful of people aimed at getting STANDARD MODEL or something more fundamental from an extremely simple toolkit. The tools are just 4-valent embedded graphs-----embedded in 3D space. So-far there has not been any need to label the edges. In a common version of Loop Gravity one describes the quantum state of geometry by a SPINNET (short for "spin network"), and the evolution of quantum state corresponds to local reconnection MOVES on the spinnet. Spinfoam formalism exists in part just to give AMPLITUDES for these reconnection moves. So Yidun Wan is dealing with something familiar, namely 4-valent spinnets. Except it is even simpler because no labeling. Just a clean 4-valent graph. Except the edges between the nodes can be TWISTED. That is a new thing, so think of them as ribbons or tubes. They have not yet got the generations of particles of the Standard Model. It is a high-risk venture. We have already discussed the earlier 2005 work of Sundance Bilson-Thompson that essentially started this line of investigation. What they are attempting is to put the Sundance particle model into the context of spinnet gravity. Note that with 4-valent graphs what one is talking about is a resolution of 3D space into tetrahedra. Each node is a tetrahedron. Each edge going out from the node is the side of that tetrahedron. The evolution moves correspond to Reidermeister moves on a simplicial manifold where one does things like the 2 <--> 3 move where two adjacent tets are divided up into 3 tets, or vice versa. Interestingly Ambjorn Loll Causal Triagulations approach to QG also uses these moves a lot in the 3D case and also uses analogous ones in the 4D case. This was a nice talk by Yidun Wan. BTW he has posted here some and also has a blog called "Road to Unification" I guess I should recall the link to Sundance Preon paper since it is a root paper for this work http://arxiv.org/abs/hep-ph/0503213 A topological model of composite preons Sundance O. Bilson-Thompson 6 pages, 4 figures (Submitted on 22 Mar 2005 (v1), last revised 27 Oct 2006 (this version, v2)) "We describe a simple model, based on the preon model of Shupe and Harari, in which the binding of preons is represented topologically. We then demonstrate a direct correspondence between this model and much of the known phenomenology of the Standard Model. In particular we identify the substructure of quarks, leptons and gauge bosons with elements of the braid group $B_3$. Importantly, the preonic objects of this model require fewer assumed properties than in the Shupe/Harari model, yet more emergent quantities, such as helicity, hypercharge, and so on, are found. Simple topological processes are identified with electroweak interactions and conservation laws. The objects which play the role of preons in this model may occur as topological structures in a more comprehensive theory, and may themselves be viewed as composite, being formed of truly fundamental sub-components, representing exactly two levels of substructure within quarks and leptons." I should warn that what Yidun is working on is not yet a particle model and it is not guaranteed to reach the goal. The Sundance work shows the possibility of getting the generations of particles out of topology, braided networks in particular. So there is some chance of success. Yidun's work is at the stage of looking at interactions between these particle-like topological configurations and how they propagate thru the rest of the spinnet, which represents the geometry of empty space. As of this talk they did not have one-to-one correspondence with particles. Or at least that is how it looked to me.