Progress on braided spin networks?

[tom.stoer]

I was always fascinated by the ideas regarding the Bilson-Thomson (+ Smolin and Markopolou) preons formed by braided structures. Has there been any progress in the last couple of month? Any deeper relation to spin networks?

 

[marcus]

I was always fascinated by the ideas regarding the Bilson-Thomson (+ Smolin and Markopolou) preons formed by braided structures. Has there been any progress in the last couple of month? Any deeper relation to spin networks?

I was fascinated by it too. I haven't noticed much activity in the past couple of years, but I coiuld have missed some significant papers.

It seems to me that Thiemann and his associates never went for it, and that Rovelli and his bunch never did either.

I think you know the names to look up on arxiv, to find out. In no particular order they are

Jonathan Hackett
Yidun Wan
Song He
Louis Kauffman
Sundance Bilson-Thompson

Whoa! There was a paper in 2009:
1. arXiv:1010.2979 [pdf, other]
Octonions
Jonathan Hackett, Louis H. Kauffman
Comments: 11 pages, 11 figures
Subjects: Mathematical Physics (math-ph)
2. arXiv:0903.1376 [pdf, other]
Particle Topology, Braids, and Braided Belts
Sundance Bilson-Thompson, Jonathan Hackett, Louis H. Kauffman
Comments: 21 pages, 16 figures
Journal-ref: J.Math.Phys.50:113505,2009
Subjects: Algebraic Topology (math.AT); General Relativity and Quantum Cosmology (gr-qc)
3. arXiv:0811.2161 [pdf, other]
Infinite Degeneracy of States in Quantum Gravity
Jonathan Hackett, Yidun Wan
Comments: 10 pages, 14 figures, v2: some clarifications, no substantial changes
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
4. arXiv:0804.0037 [pdf, other]
Particle Identifications from Symmetries of Braided Ribbon Network Invariants
Sundance Bilson-Thompson, Jonathan Hackett, Lou Kauffman, Lee Smolin
Comments: 9 pages, 7 figures
Subjects: High Energy Physics - Theory (he

I think the catch is, as you and I have noted before, it takes an embedded spin-network to have braids.
The trend (both with Thiemann and Rovelli) has been towards the abstract non-embedded spin networks. The graph hilbertspaces being even more basic. The "combinatorial" formulation.

It might be a remote possibility to get to get the "good" of braids without embedding, by extending the SU(2) group that labels the links, or by extending the intertwiners somehow. Or perhaps the intriguing partial success of the braid approach might give a clue about ways to include matter. I have no concrete idea, it's just that sometimes surprises happen. The person most apt to be thinking creatively about what could be carried over from previous braids work to a more combinatorial or algebraic formulation might be Louis Kauffman. Let's suppose he is thinking along those lines. How to get the "good" of braids without actually having a manifold embedding. What has he been doing? I will look up his papers and see if there is anything we don't already know about.

 

[marcus]

Here is Louis Kauffman's recent work:

1. arXiv:1010.2979 [pdf, other]
Octonions
Jonathan Hackett, Louis H. Kauffman
Comments: 11 pages, 11 figures
Subjects: Mathematical Physics (math-ph)
2. arXiv:1001.0354 [pdf, ps, other]
Topological Quantum Information, Khovanov Homology and the Jones Polynomial
Louis H. Kauffman
Comments: 21 pages, 5 figures, LaTeX document
Subjects: Geometric Topology (math.GT); Mathematical Physics (math-ph)
3. arXiv:0910.5891 [pdf, ps, other]
Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks
Samuel J. Lomonaco, Louis H. Kauffman
Comments: 128 graphics files
Subjects: Quantum Physics (quant-ph)
4. arXiv:0909.1672 [pdf, ps, other]
Anyonic Topological Quantum Computation and the Virtual Braid Group
H. A. Dye, Louis H. Kauffman
Comments: 14 pages, 23 figures
Subjects: Quantum Physics (quant-ph); Geometric Topology (math.GT)

What the devil is the virtual braid group?

Also why is he concerning himself with octonians?

Maybe someone else can figure out the evolutionary path which LK has taken (since 2008, when I think signs appeared that the braid-matter program had stalled.)

 

[atyy]

Unlike most of LQG ethos, this is an approach that involves unification, isn't it? So it's really like string theory in that respect. The two other LQG related approaches that involve unification are Oriti and Livine's view of group field theory, and Markopoulou's approach. Actually, Markopoulou is somehow involved with all the most interesting LQG paths - she drew the connections to the Connes approach and renormalization early (I think Rovelli is going to need GFT renormalization), then this stuff with braiding, and now emergent locality.

Let me add this to the programme:
http://arxiv.org/abs/0805.3175
Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
Fotini Markopoulou, Isabeau Prémont-Schwarz
"The recent work that has motivated the present article used a state space of embedded graphs. They found that what is conserved is the braiding of the edges of the graphs. Since there is an infinite number of braids for a finite set of graph edges, there is an infinite set of conserved quantities. It is not clear at this stage what the physical information encoded by these braids is, however, if we believe the scenario of [32, 31], this implies an infinite number of particle generations. As this may be an artifact of the embedding space and, as we discussed above, the embedding information may not be relevant at the fundamental level, we here wish to study the conserved quantities in the case of non-embedded graphs."

I think the difficulty being addressed was pointed out by:
http://arxiv.org/abs/0811.2161
Infinite Degeneracy of States in Quantum Gravity
Jonathan Hackett, Yidun Wan
"The diffculty this poses comes from the fact that these locally conserved structures correspond to an infinite number of conserved quantities that don't correspond with anything that commutes with the constraints of general relativity. This poses a significant problem in any attempt to recover the classical limit from a generic embedded spin-network - there is no reason to believe that these conserved quantities will simply cease to exist in the classical limit."

Hmmm, is symmetry breaking impossible?

I think quantum graphity and the emergent locality studies must also somehow be exploring some aspect of this - the relation to spacetime is very different from Rovellian LQG (which is manifoldy conceptually, if not technically). There's a very interesting discussion in section VIII of one of the original papers in this programme:
http://arxiv.org/abs/hep-th/0603022
Quantum gravity and the standard model
Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin
"In summary, there are distinct ways for a spacetime geometry to emerge from a quantum theory. At one end of the spectrum lies the expectation that classical spacetime geometry will emerge as the classical/low energy limit of quantum general relativity (as in Loop Quantum Gravity) or a discrete and quantum version of Einstein’s theory (as in Causal Dynamical Triangulations [19]). Matter fields are to be added and coupled to the quantum geometry. At the other end, one may expect that the emergent spacetime is the collection of events that are the interactions of the excitations of an underlying pre-spacetime quantum theory, with matter being also emergent as these same excitations. That such an emergent spacetime can be dynamical has recently been investigated in [20, 21]."

 

[MTd2]

In the most updated paper, Furey wrote on the conclusion:

"Apart from this current work, Seth Lloyd is leading
the development of the theory of Division Networks, a
model for quantum gravity in the form of a lattice gauge
theory, which is written in the Unied Theory of Ideals
formalism."

http://www.perimeterinstitute.ca/personal/cfurey/UTI20100805.pdf

So, we can see a new quantum gravity theory emerging.

 

[ensabah6]

I was always fascinated by the ideas regarding the Bilson-Thomson (+ Smolin and Markopolou) preons formed by braided structures. Has there been any progress in the last couple of month? Any deeper relation to spin networks?

Instead of starting with LQG spin networks and attempting to create braids of matter, (I call this bottom up approach)

why not drop the unproven assumption of LQG and Sundance O. Bilson-Thompson braiding and instead start with Sundance O. Bilson-Thompson braiding scheme, and the standard model,
and QFT, and ask what sort of toy model would give rise to the standard model, properties like chiral, charge, parity, and lagrangian, using Sundance O. Bilson-Thompson braiding.

In other words, what would the properties of a ribbon would be needed, using QFT, or some form of emergent physics, or NCG, so that when they twist and braid, and form groups of three, form fermions and charges, with QFT lagrangians? (top down approach)

Sundance O. Bilson-Thompson might be the correct description of the SM, and have nothing to do with LQG, the ribbons have nothing to do with spin networks.