Quantum gravity from Weyl conformal geometry
Abstract We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincaré symmetry. Weyl conformal geometry is defined by equivalence classes of the metric and Weyl gauge fi...
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2025-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14489-z |
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| author | D. M. Ghilencea |
| author_facet | D. M. Ghilencea |
| author_sort | D. M. Ghilencea |
| collection | DOAJ |
| description | Abstract We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincaré symmetry. Weyl conformal geometry is defined by equivalence classes of the metric and Weyl gauge field ( $$\omega _\mu $$ ω μ ), related by Weyl gauge transformations. Weyl geometry can be seen as a covariantised version of Riemannian geometry with respect to Weyl gauge symmetry (of dilatations). This Weyl gauge-covariant formulation of Weyl geometry is metric, which avoids century-old criticisms on the physical relevance of this geometry, that ignored its gauge symmetry. Weyl quadratic gravity and its geometry have interesting properties: (a) Weyl gauge symmetry is spontaneously broken and Einstein–Hilbert gravity and Riemannian geometry are recovered, with $$\Lambda >0$$ Λ > 0 ; (b) this is the only true gauge theory of a space-time symmetry i.e. with a physical (Weyl) gauge boson ( $$\omega _\mu $$ ω μ ); (c) all fields and masses have geometric origin (with no added scalar fields); (d) the theory has a Weyl gauge invariant geometric regularisation (by $$\hat{R}$$ R ^ ) in d dimensions and it is Weyl-anomaly free; this anomaly is recovered in the broken phase after massive $$\omega _\mu $$ ω μ decouples; (e) the theory is the leading order of the general Weyl gauge invariant Dirac-Born–Infeld (WDBI) action of Weyl conformal geometry in d dimensions; (f) in the limit of vanishing Weyl gauge current, one obtains conformal gravity; (g) finally, Standard Model (SM) has a natural embedding in conformal geometry with no new degrees of freedom, with successful Starobinsky–Higgs inflation. Briefly, Weyl conformal geometry generates a (quantum) gauge theory of gravity, given by Weyl quadratic gravity action and its WDBI generalisation, and leads to a unified description, by the gauge principle, of Einstein–Hilbert gravity and SM interactions. |
| format | Article |
| id | doaj-art-ec4676d40b0a462b94e89b520ea3a25c |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-ec4676d40b0a462b94e89b520ea3a25c2025-08-20T03:42:56ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-07-0185712410.1140/epjc/s10052-025-14489-zQuantum gravity from Weyl conformal geometryD. M. Ghilencea0Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN)Abstract We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincaré symmetry. Weyl conformal geometry is defined by equivalence classes of the metric and Weyl gauge field ( $$\omega _\mu $$ ω μ ), related by Weyl gauge transformations. Weyl geometry can be seen as a covariantised version of Riemannian geometry with respect to Weyl gauge symmetry (of dilatations). This Weyl gauge-covariant formulation of Weyl geometry is metric, which avoids century-old criticisms on the physical relevance of this geometry, that ignored its gauge symmetry. Weyl quadratic gravity and its geometry have interesting properties: (a) Weyl gauge symmetry is spontaneously broken and Einstein–Hilbert gravity and Riemannian geometry are recovered, with $$\Lambda >0$$ Λ > 0 ; (b) this is the only true gauge theory of a space-time symmetry i.e. with a physical (Weyl) gauge boson ( $$\omega _\mu $$ ω μ ); (c) all fields and masses have geometric origin (with no added scalar fields); (d) the theory has a Weyl gauge invariant geometric regularisation (by $$\hat{R}$$ R ^ ) in d dimensions and it is Weyl-anomaly free; this anomaly is recovered in the broken phase after massive $$\omega _\mu $$ ω μ decouples; (e) the theory is the leading order of the general Weyl gauge invariant Dirac-Born–Infeld (WDBI) action of Weyl conformal geometry in d dimensions; (f) in the limit of vanishing Weyl gauge current, one obtains conformal gravity; (g) finally, Standard Model (SM) has a natural embedding in conformal geometry with no new degrees of freedom, with successful Starobinsky–Higgs inflation. Briefly, Weyl conformal geometry generates a (quantum) gauge theory of gravity, given by Weyl quadratic gravity action and its WDBI generalisation, and leads to a unified description, by the gauge principle, of Einstein–Hilbert gravity and SM interactions.https://doi.org/10.1140/epjc/s10052-025-14489-z |
| spellingShingle | D. M. Ghilencea Quantum gravity from Weyl conformal geometry European Physical Journal C: Particles and Fields |
| title | Quantum gravity from Weyl conformal geometry |
| title_full | Quantum gravity from Weyl conformal geometry |
| title_fullStr | Quantum gravity from Weyl conformal geometry |
| title_full_unstemmed | Quantum gravity from Weyl conformal geometry |
| title_short | Quantum gravity from Weyl conformal geometry |
| title_sort | quantum gravity from weyl conformal geometry |
| url | https://doi.org/10.1140/epjc/s10052-025-14489-z |
| work_keys_str_mv | AT dmghilencea quantumgravityfromweylconformalgeometry |