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From what I understand, the obvious problems with a gravity being a posed as a gauge theory of the Lorentz group are the residual tetrad fields having no obvious gauge theoretic interpretation, as well as this group simply not being the full set of diffeomorphisms. Gauging the full Poincare group appears to not only consider the full set of spacetime isometries but also provides a description of the tetrad fields as gauge potentials for the translation symmetries in the group.

What are the remaining obstacles to a convincing gauge theory of gravity?

Tom Walker
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    Does this answer your question? Gravity as a gauge theory – probably_someone Apr 27 '20 at 20:33
  • See also: https://physics.stackexchange.com/questions/4359/diffm-as-a-gauge-group-and-local-observables-in-theories-with-gravity https://physics.stackexchange.com/questions/12461/argument-about-fallacy-of-diffm-being-a-gauge-group-for-general-relativity https://physics.stackexchange.com/questions/46324/to-which-extent-is-general-relativity-a-gauge-theory https://physics.stackexchange.com/questions/339699/coupling-fermions-with-gravity – user1504 Apr 27 '20 at 23:53

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