Gravi-GUT theories turn out to play a major role in the alternative physics of the past several decades. E8 theory by Garrett Lisi (
@garrett) is a gravi-GUT theory. So too, it turns out, is Eric Weinstein's Geometric Unity, by a slightly roundabout route (in GU, our 4-dimensional world is a submanifold of 14 dimensions, and GU's gauge group contains the 14-dimensional spin group Spin(7,7), which in turn contains Spin(1,3), treated as the space-time symmetry of the 4-dimensional submanifold).
For reference, I will link to a previous PF thread on the Gravi-GUT topic, and posts by Lubos Motl and Jacques Distler:
http://arxiv.org/abs/0910.5167
Gravity from a Particle Physicist's perspective
R. Percacci
Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil April 20-24 2009. To appear in
Proceedings of Science
(Submitted on 27 Oct 2009)
"In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what sense is gravity a gauge theory?" I will reformulate the theory of...
https://web.archive.org/web/2013090...m/2007/11/exceptionally-simple-theory-of.html
https://golem.ph.utexas.edu/~distler/blog/archives/002140.html
Some comments on the criticism that gravi-GUTs apriori should not work, because they violate the Coleman-Mandula theorem... The theorem says that you cannot have nontrivial combinations of space-time and gauge symmetries in a quantum field theory.
To this I would add that gravi-GUT presupposes the treatment of gravity as a gauge theory with noncompact gauge group (Lorentz gauge gravity or Poincare gauge gravity) - e.g. the SO(1,3) that Nesti and Percacci combine with GUT SO(10) to obtain gravi-GUT SO(11,3) - and this in itself seems problematic to me, because noncompactness in a gauge group should already mean vacuum instability in the quantum theory.
Gravi-GUT advocates have suggested various reasons why their theories might evade Coleman-Mandula. One is that Coleman-Mandula is about global space-time symmetries, but gravi-GUT is about locally gauged symmetries, and so if the global space-time geometry is not Minkowski space, the theorem won't apply. This seems unlikely to me - the theory doesn't work in flat space, but starts working in slight deviations from flat space? So there may be some way to extend Coleman-Mandula to nonflat geometries and to locally gauged theories of gravity.
Another would-be loophole is that the full gravi-GUT gauge group only comes to life in a "topological" phase, and that when you have a geometric phase with a nondegenerate metric, the space-time gauge symmetry and the internal gauge symmetry have already separated via symmetry-breaking. This is more sophisticated, but I'm still overall skeptical. I think in this case the unification is fictitious. In reality, you just have separate space-time and internal-quantum-number symmetries, the group that supposedly unites them plays no role in actual physics, and the topological phase is entirely counterfactual (never appears in the history of our actual universe).
As for the idea that gauge theories of gravity are inherently ill-defined quantum mechanically, it has been suggested to me that noncompactness leads to vacuum instability only in the specific case of a Yang-Mills lagrangian, and that it wouldn't be the case for gauge theories with a different Lagrangian. But e.g. SO(10) GUT is definitely a Yang-Mills theory, doesn't that mean that in SO(3,11) gravi-GUT, we're implicitly treating gravity as an SO(3,1) Yang-Mills theory?
So my overall feeling is that gauge theories of gravity and gravi-GUT theories of unification are apriori ill-defined as quantum theories, and that quantum gravity just doesn't work like that. I suspect that they survive as research programs because a true refutation of the premise would be quite subtle, and an advocate can appeal to many details and say, maybe there's a loophole there. They might even have heuristic or pedagogical value on the path to the true quantum gravity, the way that quantum field theory is often introduced by way of failed approaches that don't work, the better to motivate the ones that do.
Meanwhile, we have in addition this chiral approach to graviweak unification, in which the gravitational group is now SU(2). This is a whole new twist, because SU(2) (unlike e.g. SO(3,1)) is compact! But, the attempt to make a quantum theory using Ashtekar variables usually proceeds via the complexification of SU(2), and the complexification is noncompact. In other threads, I have taken the unusual position that loop quantum gravity, which is one attempt to build quantum gravity on Ashtekar variables, is quantum-mechanically wrong, but that quantum gravity in Ashtekar variables *can* be valid, so long as a different quantization procedure is used, one that ends up reproducing the usual quantum gravity that is based on quantizing the metric.
But overall, I'm not sure what to make of "chiral gravi-GUTs". If there's a way to show that they too are problematic, it might be via Coleman-Mandula, but we probably can't guess the details until someone shows us exactly how the quantum theory of SU(2) gauge gravity is supposed to work.
Regarding the specific model proposed by Stephon Alexander et al, in which the extra SU(2)R in Pati-Salam grand unification is going to be treated as the Ashtekar gauge field, this ought to face extra difficulties owing to the fact that within Pati-Salam, SU(2)R is already needed to supply the U(1)Y hypercharge of the standard model. Asking it to do that and be gravity at the same time, may be asking for the impossible.
