Can LSS unification (gravity, gauge, Higgs) be quantized à la new LQG ?

[marcus]

Can LSS unification (gravity, gauge, Higgs) be quantized à la "new LQG"?

This came out in April. We had it on our second quarter MIP ("most important paper") poll.
https://www.physicsforums.com/showthread.php?t=413838

http://arxiv.org/abs/1004.4866
Unification of gravity, gauge fields, and Higgs bosons
A. Garrett Lisi, Lee Smolin, Simone Speziale
12 pages
(Submitted on 27 Apr 2010)
"We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge invariant action -- an extension of the Plebanski action for general relativity -- we recover the action for gravity, Yang-Mills, and Higgs fields. The low-energy coupling constants, obtained after symmetry breaking, are all functions of the single parameter present in the initial action and the vacuum expectation value of the Higgs."
...

So far, this is a classical treatment. And it uses a spacetime manifold. The basic playground is a manifold M with a principle G-bundle over M where G can be, for example, Spin(1+N,3). This how I read it anyway.

We know that in some cases we can start with that kind of picture and in the course of constructing a quantum version, get a "manifoldless spacetime" picture using graphs, spin networks and spinfoams. Then, instead of a spatial or spacetime continuum one has (for each graph) a group manifold---a finite cartesian product of the basic group G. These provide a way to set up graph Hilbert spaces and then one takes a projective limit.

I haven't thought about how much of that might go over using a different group such as Spin(1+N,3).

I just toss this out in case anyone wants to have a look at the Lisi, Smolin, Speziale paper and speculate about a "manifoldless" quantum version in the style of the new formulation of LQG we got in http://arxiv.org/abs/1004.1780

 

[marcus]

Just to be clear about it, in case a new person does not realize this, when I say "quantize" I do not mean in any conventional textbook sense. I mean construct a quantum version of the "new LQG" kind that has the right limit behavior---corresponding to what you started with.

By way of illustration: contemporary LQG is not some sort of methodical quantization of Ashtekar General Relativity (the connection version of classical GR). The field did indeed start out in the 1990s based on Ashtekar GR. But convergence of various attempts crystalized in a de novo reformulation different from, but combining aspects of each. Something like a leap occurred, as is described in the survey/status report http://arxiv.org/abs/1004.1780.

In other words, can you adapt http://arxiv.org/abs/1004.1780 to achieve a quantum theory version of the Lisi Smolin Speziale unification?