gaugegravity

Gauge gravity is a framework in theoretical physics in which gravity is formulated as a gauge theory of a spacetime symmetry group. Instead of treating the gravitational field solely as the metric of spacetime, gauge gravity assigns gauge fields to local spacetime transformations, typically translations and Lorentz rotations. The primary dynamical variables are a tetrad (vierbein) field e_mu^a, associated with local translations, and a spin connection ω_mu^{ab}, associated with local Lorentz rotations. From these, curvature and torsion arise as field strengths, encoding gravitational effects.

Historically, the program began with Utiyama's 1956 proposal to gauge the Poincaré group, refined by Kibble and Sciama, leading to Poincaré gauge theory. In such theories, torsion is generally nonzero and couples to spin density, while energy-momentum sources couple to the tetrad. If torsion is constrained to vanish and the action is chosen to reproduce the Einstein-Hilbert term, one recovers general relativity; more generally, the framework encompasses Einstein-Cartan theory and other gravity models, including teleparallel gravity, where curvature vanishes and gravity is encoded in torsion.

Variants and related ideas include de Sitter or affine gauge gravity, metric-affine gravity, and teleparallel or symmetric teleparallel theories. Gauge gravity provides a platform for unifying gravity with the gauge principles behind the standard model, and for exploring gravity with torsion, spinor couplings, and possible quantum extensions.

Current status: gauge gravity remains an active area of research, with no direct experimental evidence distinguishing it from GR in standard regimes. It offers alternative viewpoints on the geometric meaning of gravity and potential routes to quantum gravity.