Anomaly-free scale symmetry and gravity
arXiv:2201.09232 · doi:10.1016/j.physletb.2023.137898
Abstract
In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We show that conformal symmetry can be made free from the quantum anomaly only in the flat space. The presence of gravity would reduce the global symmetry group of the fundamental theory to the scale invariance only. We discuss how the effective Lagrangian respecting the scale symmetry can be used for the description of particle phenomenology and cosmology.
arXiv commentAn error in the generic solution for anomaly-free Weyl transformation is corrected. The updated conclusion is that gravity reduces conformal symmetry to the scale symmetry
References in corpus (18)
- Cosmology and the Fate of Dilatation Symmetry
- The MSM, Dark Matter and Baryon Asymmetry of the Universe
- The MSM, Dark Matter and Neutrino Masses
- The role of sterile neutrinos in cosmology and astrophysics
- Twenty Years of the Weyl Anomaly
- Quantum scale invariance, cosmological constant and hierarchy problem
- Scale invariance, unimodular gravity and dark energy
- Higgs-Dilaton Cosmology: From the Early to the Late Universe
- Weyl-Gauging and Conformal Invariance
- Higgs-Dilaton Cosmology: an effective field theory approach
- No fifth force in a scale invariant universe
- BRST approach to Lagrangian construction for bosonic continuous spin field
- Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation
- Weyl vs. Conformal
- Restricted Weyl invariance in four-dimensional curved spacetime
- Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
- Conformal symmetry: towards the link between the Fermi and the Planck scales
- Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance