Is the spin connection confined or condensed?

TL;DR

This paper explores the possibility that the spin connection in gravity, viewed as a nonabelian gauge field, could be confined or condensed, potentially eliminating the need for the metricity assumption in the theory.

Contribution

It proposes that the spin connection might be confined like other nonabelian gauge fields, offering a new perspective on the role of metricity in gravity theories.

Findings

Spin connection has a negative beta function, indicating asymptotic freedom.

Confinement of the spin connection could remove the need for metricity.

Potential for a reformulation of gravity without explicit spin connection presence.

Abstract

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.