I think we are going to be following this EPRL/FK Group Field Theory development some. I will get the abstract of the earlier paper that they refer to a lot in this one. Their reference [9].
Also we should note where their terminology differs slightly from Rovelli's "marseille" vocabulary. Rovelli says a spinfoam is made of vertices edges and faces.
Rivasseau's team says:
vertices
stranded lines (also called 'propagators')
faces (= closed circuit of strand)
It is very simple. In a 4D world, for example, all the edges are like 4-lane highways.
And you don't have to draw in the faces because a face is defined by the fact that one of the lanes splits off at a vertex and loops around it. The faces are just the places where a strand loops around and makes a circuit.
It is just a different
notation for essentially the same spinfoam idea. What they call "stranded lines" are what I am imagining as 4-lane highways. There are some pictures here, on pages 3 and 4 and following:
http://arxiv.org/abs/1007.3150
Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
Thomas Krajewski, Jacques Magnen, Vincent Rivasseau, Adrian Tanasa, Patrizia Vitale
35 pages, 5 figures
(Submitted on 19 Jul 2010)
"We investigate the group field theory formulation of the EPRL/FK spin foam models. These models aim at a dynamical, i.e. non-topological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory amplitudes and compare it with existing results, in particular for a second order correction to the EPRL/FK propagator."
This LQG spinfoam GFT initiative from Rivasseau's group (Paris, Orsay) is a fairly new development. As far as I know that July 2010 paper was the first. And this one, that prompted starting this thread, is the second:
http://arxiv.org/abs/1008.0354
EPRL/FK Group Field Theory
Joseph Ben Geloun, Razvan Gurau, Vincent Rivasseau
20 pages, 2 figures
(Submitted on 2 Aug 2010)
"The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model."