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Is the spin connection confined or condensed?
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The spin connection enters the theory of gravity as a nonabelian gauge field associated with local Lorentz transformations. Normally it is eliminated from making an extra assumption - that of the metricity of the vierbein field. However, treated by itself with the usual gauge action, it has a negative beta function, implying that it is asymptotically free. I suggest that the spin connection could be confined (or perhaps partially confined) in the same way as other nonabelian gauge fields. This would remove the need to make the extra assumption of metricity, as the spin connection would not be present in the low energy theory, leaving the symmetry to be realized only using metric variables.
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Cited by 1 Pith paper
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From the Unification of Conformal and Fuzzy Gravities with Internal Interactions to the $SO(10)$ GUT and the Particle Physics Standard Model
One-loop gauge coupling running gives intermediate scales from 10^10 to 10^13 GeV and GUT scales from 10^15 to 2x10^16 GeV for four SO(10) breaking chains of the conformal-gravity unification, with two high-scale scen...
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