Baratin and Freidel: a spin foam model of ordinary particle physics

John Baez

With any luck, sometime soon you can read this paper on the arXiv:

Aristide Baratin and Laurent Freidel Hidden quantum gravity in 4d
Feynman diagrams: emergence of spin foams

The idea is that any ordinary quantum field theory in 4d Minkowski
spacetime can be reformulated as a spin foam model. This spin foam
model is thus a candidate for the G -> 0 limit of any spin foam model of
quantum gravity and matter!

In other words, we now have a precise target to shoot at. We don't know
which if any spin foam model gives gravity in 4 dimensions, but now we
know one that gives the G -> 0 limit of gravity: i.e., ordinary quantum
field theory. So, we should make up a spin foam model that reduces to
Baratin and Freidel's when G -> 0.

The fascinating thing I noticed is that their spin foam model seems to
be based on the Poincare 2-group. I invented this 2-group in my first
paper on higher gauge theory:

http://www.arxiv.org/abs/hep-th/0206130

and Marnie Sheppeard and Louis Crane wrote a paper proposing a spin foam
model based on this 2-group:

http://www.arxiv.org/abs/math.QA/0306440

The physical meaning of their spin foam model was unclear, and some
details were not worked out, but it was very tantalizing. What did it
mean??

I now conjecture - and so do Baratin and Freidel - that when everything
is properly worked out, Crane and Sheppeard's spin foam model is the
same as Baratin and Freidel's. So, it gives ordinary particle physics
in Minkowski spacetime, at least after matter is included (which Baratin
and Freidel explain how to do).

If this is true, one can't help but dream...

... that deforming the Poincare 2-group into some sort of "quantum
2-group" could give a more interesting spin foam model: ideally,
something that describes 4d quantum gravity coupled to matter! This
more interesting spin foam model should reduce to Baratin and Freidel's
in the limit G -> 0.

Of course this dream sounds "too good to be true", but there are some
hints that it might work, to be found in the paper by Freidel and
Starodubtsev:

http://arxiv.org/abs/hep-th/0501191

In particular, they describe gravity in way (equation 26) which reduces
to BF theory as G -> 0. BF theory is a theory of flat spacetime and
that's what Baratin and Freidel's spin foam model describes. So, it may
all fit together.

Optimistic hopes in quantum gravity are usually dashed, but stay tuned.