Current Status of Loop Quantum Gravity: Successes, Failures & Open Questions

[maline]

Where does the LQG approach stand right now? What are its biggest successes and failures? Does it have any known difficulties that might be "fatal"? What major questions (on the fundamental level) are still open in the approach, and is there "momentum" toward solving them?

In particular, is it possible that LQG + SM + [some simple dark matter candidate] can give a complete and consistent model for all of elementary physics? If not, what is missing?

 

[atyy]

I'm not sure. I did a quick check and found these.

https://arxiv.org/abs/1812.02110
Emergent 4-dimensional linearized gravity from spin foam model
Muxin Han, Zichang Huang, Antonia Zipfel

https://arxiv.org/abs/1810.09364
Bubble Networks: Framed Discrete Geometry for Quantum Gravity
Laurent Freidel, Etera R. Livine

https://arxiv.org/abs/1803.10289
Emergence of Spacetime in a restricted Spin-foam model
Sebastian Steinhaus, Johannes Thürigen

https://arxiv.org/abs/1808.01252
A review on Loop Quantum Gravity
Pablo Antonio Moreno Casares

 

[maline]

https://arxiv.org/abs/1808.01252
A review on Loop Quantum Gravity
Pablo Antonio Moreno Casares

Thanks! The last chapter in this reference (list of open problems) was very helpful in getting an overview of the situation, although I haven't studied the theory itself and so I couldn't understand the issues in any detail.
I'd love to hear from an "insider", especially if they are able to address my level of knowledge (standard coordinate-based GR, and QFT at the level of Weinberg Vol.1)

 

[king vitamin]

In particular, is it possible that LQG + SM + [some simple dark matter candidate] can give a complete and consistent model for all of elementary physics? If not, what is missing?

I'm not very familiar with LQG, but the SM (and any dark matter candidate which is described by QFT) is not an object which is understood to arbitrary energies. People don't know if the current theory even makes sense at high energy scales. So one would at least need to show that these QFTs are well-behaved in the UV, which is a hard problem.

And although I am not familiar with LQG, I'm familiar enough with the current state of quantum gravity to know that no theory is in a place where it can make definite unequivocal predictions about interesting problems (like early cosmology or late-time black hole evaporation).

 

[maline]

So one would at least need to show that these QFTs are well-behaved in the UV, which is a hard problem.

Well, that is one major achievement that LQG wishes to claim! Giving spacetime a discrete structure is expected to make all UV problems disappear. Part of my question is whether we can state confidently that LQG does accomplish this, and whether the resulting finite QFT has been worked out in any detail (say, determining "true fundamental values" for coupling constants).

 

[mitchell porter]

Judging by citations, there is no sign of progress on the fermion doubling problem since Barnett and Smolin 2015, an utterly basic issue if you want to couple the SM to LQG, since the SM is a chiral theory. Their paper is about the Hamiltonian approach to LQG, the spin-foam approach might be better here but I don't know any details.

Eichhorn and Lippoldt remark that fermion doubling is liable to be a problem for any approach to quantum gravity that discretizes space. They work on asymptotic safety, and certainly, if you want an approach to quantum gravity other than string theory, I think asymptotic safety must now be counted as the leading alternative. Personally I am also interested in Salvio and Strumia's adimensional gravity or agravity, Dubovsky et al's "TT bar" deformation of gravity, and probably other esoteric approaches I can't think of right now.

 

[atyy]

Judging by citations, there is no sign of progress on the fermion doubling problem since Barnett and Smolin 2015, an utterly basic issue if you want to couple the SM to LQG, since the SM is a chiral theory. Their paper is about the Hamiltonian approach to LQG, the spin-foam approach might be better here but I don't know any details.

Eichhorn and Lippoldt remark that fermion doubling is liable to be a problem for any approach to quantum gravity that discretizes space. They work on asymptotic safety, and certainly, if you want an approach to quantum gravity other than string theory, I think asymptotic safety must now be counted as the leading alternative. Personally I am also interested in Salvio and Strumia's adimensional gravity or agravity, Dubovsky et al's "TT bar" deformation of gravity, and probably other esoteric approaches I can't think of right now.

There is an attempt to solve the fermion doubling problem here - not in quantum gravity, but in an approach that discretizes space: https://arxiv.org/abs/1809.11171.

 

[Demystifier]

There is an attempt to solve the fermion doubling problem here

I never completely understood why exactly is it a problem. If you regularize Dirac equation on a lattice, you get some doublers that were not present in the original continuous theory. But those doublers are only relevant at very large momenta, proportional to the inverse lattice spacing. Hence they are not relevant to the low momenta phenomenology, so no contradiction with existing experiments appears. So where is the problem?

 

[king vitamin]

Well, that is one major achievement that LQG wishes to claim! Giving spacetime a discrete structure is expected to make all UV problems disappear. Part of my question is whether we can state confidently that LQG does accomplish this, and whether the resulting finite QFT has been worked out in any detail (say, determining "true fundamental values" for coupling constants).

I see. If LQG does actually provide a unique UV completion to the QFTs which live on its spacetime, then there's certainly an enormous amount of work needed to determine what that UV behavior is. Just working on the UV behavior of LQG alone without also understanding the behavior of everything else will not give us detailed high-energy predictions, because on general grounds we expect the degrees of freedom of LQG and QFT to both be important at those scales.

I never completely understood why exactly is it a problem. If you regularize Dirac equation on a lattice, you get some doublers that were not present in the original continuous theory. But those doublers are only relevant at very large momenta, proportional to the inverse lattice spacing. Hence they are not relevant to the low momenta phenomenology, so no contradiction with existing experiments appears. So where is the problem?

At least with massless chiral fermions, my understanding is that the doublers are also massless (they are chiral fermions of opposite handedness). So a theory like the Standard Model, where there are only massless left-handed leptons, cannot be obtained from a lattice (or perhaps LQG in light of Barnett+Smolin) regularization.

 

[atyy]

I never completely understood why exactly is it a problem. If you regularize Dirac equation on a lattice, you get some doublers that were not present in the original continuous theory. But those doublers are only relevant at very large momenta, proportional to the inverse lattice spacing. Hence they are not relevant to the low momenta phenomenology, so no contradiction with existing experiments appears. So where is the problem?

The Wang and Wen paper introduction sets up the problem as remaining for the low energy regime when chiral fermions interact with non-abelian gauge fields (they only mention gauge fields, but I remember reading elsewhere that it's the non-abelian case for which the problem remains).

Here is another place where he states the problem within the string net language https://arxiv.org/abs/1210.1281 (note 52 on p39) "So far we can use string-net to produce almost all elementary particles, expect for the graviton that is responsible for the gravity. Also, we are unable to produce the chiral coupling between the SU(2) gauge boson and the fermions within the string-net picture."

 

[Demystifier]

At least with massless chiral fermions, my understanding is that the doublers are also massless (they are chiral fermions of opposite handedness). So a theory like the Standard Model, where there are only massless left-handed leptons, cannot be obtained from a lattice (or perhaps LQG in light of Barnett+Smolin) regularization.

Yes, but note that doublers live in a regime where standard Lorentz invariance is strongly violated (due to the cutoff). So we cannot use the usual Lorentz-invariant argument that the doublers should be seen at low momenta because they are massless. The mass in Lorentz-non-invariant theories has a very different meaning than that in Lorentz-invariant ones.