Eur. Phys. J. C (2017) 77: 605
https://doi.org/10.1140/epjc/s10052-017-5183-0

Regular Article - Theoretical Physics

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

¹ Theoretical Particle Physics and Cosmology Group, Department of Physics, King’s College London, Strand, London, WC2R 2LS, UK
² Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada

^* e-mail: marco.de_cesare@kcl.ac.uk

Received: 1 May 2017
Accepted: 31 August 2017
Published online: 14 September 2017

Abstract

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl’s original proposal.