PCF Pure Connection Formulation of GR now QG: Krasnov Delfino Scarinci

[marcus]

http://arxiv.org/abs/1306.4035
Graviton scattering amplitudes and Pure Connection Formulation of GR
Gianluca Delfino
(Submitted on 17 Jun 2013)
We show how the recently introduced "Pure Connection Formulation" of gravity provides a natural framework for approaching the problem of computing graviton scattering amplitudes. In particular, we show that the interaction vertices are greatly simplified in this formalism as compared to the Einstein-Hilbert perturbation theory. This, in turns, leads to very simple Feynman rules that we employ for the direct computations. Furthermore, this framework naturally extends to wider class of gravitational theories, which encompasses General Relativity as a special case. We compute all the possible tree-level graviton-graviton scattering amplitudes for a general theory from this class. In the GR case the results are in complete accordance with the known expressions in the literature. Moreover, for the general theory distinct from GR, we find new tree-level parity-violating amplitudes. The presence of this new amplitudes is a direct consequence of the fact that the general theory does not exhibit explicit parity invariance.
122 pages, PhD Thesis

 

[marcus]

The catch is that AFAIK they have not yet put in MATTER.
But it's still early. So far most of the papers on PCF are by Krasnov solo.
Krasnov and Delfino are at Nottingham.
Scarcini got his degree at Nottingham in 2012 and is now PD at Erlangen (Thiemann group).

Here is an earlier paper:
http://arxiv.org/abs/arXiv:1210.6215
Pure connection formalism for gravity: Feynman rules and the graviton-graviton scattering
Gianluca Delfino, Kirill Krasnov, Carlos Scarinci
(Submitted on 23 Oct 2012)
We continue to develop the pure connection formalism for gravity. We derive the Feynman rules for computing the connection correlation functions, as well as the prescription for obtaining the Minkowski space graviton scattering amplitudes from the latter. The present formalism turns out to be significantly simpler than the one based on the metric in many aspects. The most drastic difference with the usual approach is that the conformal factor of the metric, which is a source of difficulties in the metric treatment, does not propagate in the connection formulation even off-shell. This simplifies both the linearized theory and the interactions. For comparison, in our approach the complete off-shell cubic GR interaction contains just 3 terms, with only a single term relevant at tree level. This should be compared to at least a dozen terms in the metric formalism. We put the technology developed to use and compute the simplest graviton-graviton scattering amplitudes. For GR we reproduce the well-known result. For our other, distinct from GR, interacting theories of massless spin 2 particles we obtain non-zero answers for some parity-violating amplitudes. Thus, in the convention that all particles are incoming, we find that the 4 minus, as well as the 3 minus 1 plus amplitudes are zero (as in GR), but the amplitudes with 4 gravitons of positive helicity, as well as the 3 plus 1 minus amplitudes are different from zero. This serves as a good illustration of the type of parity violation present in these theories. We find that the parity-violating amplitudes are important at high energies, and that a general parity-violating member of our class of theories "likes" one helicity (negative in our conventions) more than the other in the sense that at high energies it tends to convert all present gravitons into those of negative helicity.
46 pages, figures

They find an infinite family of theories with massless spin-2 particles. So they point out that this is not unique to GR.

If your theory has a massless spin-2 graviton, that's nice, but it does not mean that your theory recovers GR.

Many people seem to think it does (Krasnov et al comment) but in fact it does not. They show an abundance of counter-examples.

Interesting paper. Krasnov is one of the invited plenary speakers scheduled to speak at Loops 2013 conference in July. I suppose he may talk about PCF.

 

[julian]

Sounds really interesting! Do they make reference to already put in place schemes for calculating scattering amplitudes of Rovelli et al? The matter question I've been wondering about as well if anybody has done that or if people are still concentrating of gravity. Is incorporating matter more difficult? Why is that do you know?

 

[julian]

"If your theory has a massless spin-2 graviton, that's nice, but it does not mean that your theory recovers GR."

I remember the paper "From Gravitons to Gravity: Myths and Reality" arXiv:gr-qc/0409089 that provides a discussion on this.

 

[marcus]

Sounds really interesting! Do they make reference to already put in place schemes for calculating scattering amplitudes of Rovelli et al?

They refer to graviton amplitudes calculated earlier (2002) in perturbative QG by Zvi Bern, before Rovelli et al made the calculation in the nonperturbative LQG context.
[10] Zvi Bern. Perturbative quantum gravity and its relation to gauge theory. Living Rev.Rel., 5:5, 2002, gr-qc/0206071.

I haven't looked at the Zvi Bern paper. Delfino (whose reference [10] this is) says that the amplitudes he calculates AGREE with what is in the 2002 paper.

I think of a graviton as native to the perturbation theory context, so it seems reasonable to want to compare results with perturbative QG calculations.

BTW I remember that paper by Thanu Padmanabhan too! It caused a stir when it came out
Krasnov PCF goes further, though, in at least one sense: they offer an infinite class of counterexamples---theories which are NOT GR but which still have a massless spin 2 particle.