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Quantum gravity from Weyl conformal geometry.

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Title: Quantum gravity from Weyl conformal geometry.
Authors: Ghilencea, D. M.1 (AUTHOR) dumitru.ghilencea@cern.ch
Source: European Physical Journal C -- Particles & Fields. Jul2025, Vol. 85 Issue 7, p1-24. 24p.
Subjects: Quantum gravity, Conformal geometry, Particle physics, Weyl groups, Riemannian geometry, Gauge field theory, Clifford algebras
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 ( 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 Λ > 0 ; (b) this is the only true gauge theory of a space-time symmetry i.e. with a physical (Weyl) gauge boson ( 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 R ^ ) in d dimensions and it is Weyl-anomaly free; this anomaly is recovered in the broken phase after massive 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. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Quantum gravity from Weyl conformal geometry.
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  Data: 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 ( 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 Λ > 0 ; (b) this is the only true gauge theory of a space-time symmetry i.e. with a physical (Weyl) gauge boson ( 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 R ^ ) in d dimensions and it is Weyl-anomaly free; this anomaly is recovered in the broken phase after massive 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1140/epjc/s10052-025-14489-z
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        Text: English
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      – SubjectFull: Conformal geometry
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      – SubjectFull: Particle physics
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      – SubjectFull: Weyl groups
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      – SubjectFull: Riemannian geometry
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      – SubjectFull: Gauge field theory
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              Text: Jul2025
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              Y: 2025
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