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

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.

11 pages; v2: matches published version in EPJC; new title, includes new sections on the coupling of matter fields to the extended gravitational sector

References in corpus (6)

• Conformal Symmetry and the Standard Model
• Metric-affine f(R) theories of gravity
• Scale invariance, unimodular gravity and dark energy
• Implication of Compensator Field and Local Scale Invariance in the Standard Model
• Quantum propagation across cosmological singularities
• Spectral action with zeta function regularization

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• Standard Model in Weyl conformal geometry
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• Weyl $R^2$ inflation with an emergent Planck scale
• Dark matter as a Weyl geometric effect
• Weyl Connections and their Role in Holography
• Non-metric geometry as the origin of mass in gauge theories of scale invariance
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Conformally invariant proper time with general non-metricity
• Note on the absence of the second clock effect in Weyl gauge theories of gravity
• The origin of Weyl gauging in metric-affine theories
• Chiral gauge theory and gravity from unconventional supersymmetry
• A generalized Weyl structure with arbitrary non-metricity
• Noncommutative gravity with self-dual variables
• BRST Formalism of Weyl Conformal Gravity
• Inflation in Weyl Scaling Invariant Gravity with $R^3$ Extensions
• Conformal inflation with chameleon coupling
• Tolman-Ehrenfest-Klein Law in non-Riemannian geometries
• Higgs Potential from Weyl Conformal Gravity
• Non-metricity signatures on the Higgs boson signal strengths at the LHC