Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection?

We question the status of TEGR, the Teleparallel Equivalent of General Relativity,
as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present
a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field). We point out that, while it is usually presented as absent, the gauging of the


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