Progress in metric-affine gauge theories of gravity with local scale invariance

Abstract

Einstein's general relativity theory describes very well the gravitational phenomena in the macroscopic world. In the microscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for a renormalizable field theory. We argue that the local extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to a GL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status of independent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein "s GR surfaces as an effective "lowenergy" theory.

Hyperfluid — a model of classical matter with hypermomentum

“…The metric g αβ is a 0-form, the coframe ϑ α and the connection Γ α β are 1-forms. The list of the field strengths includes the nonmetricity 1-form Q αβ := −Dg αβ besides the 2-forms of torsion T α and curvature R α β [18,19].…”

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)]

“…[17].) Both constraints satisfy Yang's equation (2) due to the Bianchi identity (25) for the Lie dual of the curvature as well as the condition (3) of vanishing gauge field energy, typical for instantons. According to (29) the first case corresponds to Einstein spaces, annihilating the corresponding partially topological action, whereas the selfdual case induces Thompson spaces [61].…”

“…(sponteneous) symmetry breaking of the scale or Weyl invariance of the original Lagrangian L QPG related to (14), for instance in a model [25] dynamically coupled to a dilaton field ϕ, cf. Ref.…”

“…In 1974 Yang proposed an affine gauge theory gravity [70] which, due to its scale invariance, can be regarded as a rather promising fundamental theory of (quantum) gravity in the high-energy limit [25], without invoking extra dimensions or supersymmetry, cf. Ref.…”

“…Recent torsion balance experiments [28] have probed the inverse square law and found no deviation even below the hypothetical dark energy (DE) scale of λ DE = (hc/ρ DE ) 1/4 ≃ 85 µm. Thus this 'window' of possibly new gravitational physics seems also to be closing.In 1974 Yang proposed an affine gauge theory gravity [70] which, due to its scale invariance, can be regarded as a rather promising fundamental theory of (quantum) gravity in the high-energy limit [25], without invoking extra dimensions or supersymmetry, cf. Ref.…”