Conformal geometry as the gauge theory beyond Einstein gravity and the Standard Model

Weyl conformal geometry can be regarded as a gauge theory of the Weyl group (of Poincare and dilatation symmetries) and is defined by equivalent classes of the metric and Weyl gauge boson of dilatations (ω_μ​), related by Weyl gauge transformations. The associated action with this gauge symmetry is the vector-tensor Weyl quadratic gravity. I will show the existence of a manifestly Weyl gauge-covariant formulation of this geometry, in which this geometry is actually metric, thus avoiding a century-old criticism of Einstein. Weyl gauge symmetry is broken à la Stueckelberg, ω_μ​ becoming massive and decoupling, to recover Einstein gravity in the broken phase, corresponding to a transition from conformal geometry/connection to Riemannian geometry/connection. Weyl gauge symmetry is also free of the Weyl anomaly, recovered in the broken phase after the massive ω_μ​ decouples. The action has a non-perturbative UV completion in a Weyl gauge invariant DBI-like action associated to conformal geometry. No scalar fields compensators or UV regulators are required. The Standard Model (SM) admits a natural embedding in conformal geometry, with no new degrees of freedom beyond SM and Weyl geometry. The implications of this embedding are briefly addressed.