Note: I don't know much about QFT, aside from some basics, I am a student and first and foremost a student of GR.
As far as I am aware, the fact that interactions are gauge theories allow some pretty natural ways of deriving them. For example, for QED, if one is given a matter field $\phi$ (matter here can be bosons as well), whose lagrangian is invariant under global $U(1)$ transformations, then demanding that this lagrangian should be invariant under $U(1)$ transformations that depend on spacetime points as well naturally leads to the introduction of an $U(1)$ gauge connection, and then conjuring up a gauge-invariant lagrangian for the gauge connection too gives one a system of Maxwell's equations being coupled to the dynamics of a matter field.
Since we know from classical electrodynamics that only charged particles interact electromagnetically, this also gives a natural way of telling which particle is charged. A particle is charged if the corresponding matter field admits a global $U(1)$ symmetry.
For example the complex scalar field $$\mathcal{L}_{KG\ (C)}=\partial_\mu\phi^\dagger\partial^\mu\phi-m\phi^\dagger\phi$$ is charged but the real version of the same thing isn't.
Now, assume that one does not know about Riemannian geometry or general relativity, but because all other interactions arise via a gauge principle like in QED, this person tries to give rise to a theory of gravity the same way.
One knows that gravity interacts with everything, so one cannot use some fancyful gauge group $G$, because every matter field needs to know this symmetry. One fundamental requirement of relativistic field theories is that the action should be Lorentz-invariant, so the only Lie group that satisfies this requirement is the Lorentz group, therefore one needs to gauge the Lorentz group.
The Lorentz group is however an "external" symmetry group, not an "internal" one, eg. Lorentz transforms are related to spacetime geometry.
It is clear that the usual way of doing stuff, namely to replace $\partial_\mu$ with some gauge connection $D_\mu$ won't work here. For example in SR, the coordinates $x^\mu$ form a 4-vector. What is the meaning of a position dependent transform $\Lambda^\mu_{\ \nu}(x)x^\nu$? Nothing.
Of course, if one does know Riemannian geometry and GR, one can see that you need to give up flat spacetime one way or another. The preferred way to do that (preferred in the sense of following the example of QED or QCD) is to make Lorentz symmetry "internal" and have every Lorentz tensor $S_{\mu\nu...}$ replaced with some "section" $S_{a,b...}$ and provide a function $\theta^a_{\mu}$ that relates the "internal" and "external" spaces to one another (a vielbein, basically, but I am using its interpretation as a solder form here) and also replace the volume element $d^4x$ with the invariant volume element $\det(\theta)d^4x$ and all "spacetime" indices $\mu,\nu$ should be interpreted as referring to a general coordinate system, and of course, one needs to introduce a gauge connection $D_\mu=\delta^a_b\partial_\mu+\omega_{\mu\ \ b}^{\ a}$ instead of $\partial_\mu$, but these steps do not follow naturally from the idea of making Lorentz transformations local.
Question: Assuming one does not know GR or differential geometry, but has the bright idea of creating a gauge theory of gravity by gauging the Lorentz group, is there any "natural" way of performing this gauging that leads to a consistent field theory of gravity that couples to everything?
If so, is this necessarily unique? I guess not, since it is not a fundamental requirement to have the gauge connection determined uniquely by the vielbein (Einstein-Cartan theory for example).
But is it necessary to have a vielbein actually appear? Is it possible to arrive at this purely from the idea of gauging the Lorentz group?
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