Is the spin connection confined or condensed?

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.

6 pages - some new references, Euclidean discussion enhanced and partial-Euclidean discussion removed

References in corpus (4)

• EPFL Lectures on General Relativity as a Quantum Field Theory
• Quadratic gravity: from weak to strong
• Quartic propagators, negative norms and the physical spectrum
• A conformal model of gravitons

Cited by in corpus (13)

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• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Weyl Gravity Revisited
• Massive poles in Lee-Wick quantum field theory
• Inducing the Einstein action in QCD-like theories
• A conformal model of gravitons
• Quadratic gravity in first order formalism
• Regular black hole from a confined spin connection in Poincare gauge gravity
• Pure gauge theory for the gravitational spin connection
• Unification of Conformal and Fuzzy Gravities with Internal Interactions resulting in SO(10) and a Possible Probe through Stochastic Gravitational Wave Background