What is the status of gauged gravity

Question

The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory.

We might be able to quantize gravity similarly. Gravity might be treated as a force, instead of spacetime curve as in general relativity. I know little about gauged gravity theory. What is the current status? Who are working on it? Is it really worthwhile to pursue now?

This post imported from StackExchange Physics at 2014-10-11 09:55 (UTC), posted by SE-user Drake Marquis

Comments

Did you see physics.stackexchange.com/q/71476? As for the question whether it is worth pursuing... that's has to be your own choice, because it will probably take the rest of your life to find out. Gravity has been a tough nut for the past four centuries and it would take an extraordinary amount of optimism to pretend that it won't take at least a fifth.

This post imported from StackExchange Physics at 2014-10-11 09:55 (UTC), posted by SE-user CuriousOne

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@CuriousOne I find your comment to be very vague and influenced by the popular science media. What do you mean by "cracking" gravity? Finding an (in-theory exact) non-perturbative quantum mechanical description of relativistic gravity? In that case, no force has really been cracked, since the Standard Model is also a perturbative model.

The comment also seems to be going off on a totally different line (which isn't even a tangent) to what the question is asking for. The question is asking, I think, if field-theoretic gravity has any physical importance, not if you think the OP should study it.

Answer 1

It is standard that the Einstein-Hilbert action admits a first-oder formulation in which the field of gravity is a \(ISO(n,1)\)-Cartan connection, hence essentially a gauge field for the Poincaré group (aka "spin connection"). This is understood since the 1920s. In fact supergravity is essentially always written in this form (then for the super Poincaré group), since one needs the vielbein of the first order formalism to write down the fermionic terms. An excellent account of this is in the textbook "Superstrings and Supergravity" by D'Auria-Fré. (It's out of print, though, if you don't manage to get hold of a copy, try sending me an email.)

Comments

Just for reference: What goes wrong if one naively tries to quantize this first-order formulation of gravity? Is the theory non-renormalizable?

Answer 2

What do you mean by "pursue"? If you mean trying to produce a full-fledged theory of quantum gravity that can be "directly added" to the standard model, it's most likely not worth to "pursue". See for instance, this "proof".

But often, we can use theories which are actually inconsistent, but can give some meaningful results that can be used to test more complete theories. An obvious example that comes to my mind is Supergravity.

Similarly, trying to quantise gravity like any other force can actually yield meaningful results, making it certainly worthwhile to pursue. For instance, one may calculate graviton-graviton scattering amplitudes at the tree level, and see if the same predicted by string theory reduces to this when one takes the limit as \(\alpha'\to0\) - the exact factor by which one multiplies the stringy prediction by to get the field theory prediction is:

\( \frac{{\Gamma \left( {1 + \frac{{\alpha '}}{4}s} \right)\Gamma \left( {1 + \frac{{\alpha '}}{4}t} \right)\Gamma \left( {1 + \frac{{\alpha '}}{4}u} \right)}}{{\Gamma \left( {1 - \frac{{\alpha '}}{4}s} \right)\Gamma \left( {1 - \frac{{\alpha '}}{4}t} \right)\Gamma \left( {1 - \frac{{\alpha '}}{4}u} \right)}}\)

Take the field-theoretic limit and this approaches 1 (obviously) with no dependence on s, t, or u. See Mohaupt's lecture notes on string theory for more details.

So to answer your question, yes it is worthwhile, but not as a theory of quantum gravity on its own right.

Comments

@downvoters Could you please explain your downvote?

Answer 3

As far as I know there is a model of gauge gravity in geometric algebra, where the solutions look more like newtonian physics or at least much much simpler. http://geocalc.clas.asu.edu/pdf/GTG.w.GC.FP.pdf