The fall and the rise of Weyl gauge theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915924318093312 |
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| author | Ghilencea, D. M. |
| author_facet | Ghilencea, D. M. |
| contents | In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of a spacetime symmetry, the Weyl gauge theory (of dilatations and Poincaré symmetry). The initial physical interpretation of his theory was however short-lived and led to the downfall of Weyl geometry as a physical theory. We review how this action was re-born into a physical Weyl gauge theory of gravity. This is the only gauge theory of a spacetime symmetry with a physical gauge boson, is Weyl anomaly-free, has {\it exact} geometric interpretation, with all scales of geometric origin, and generates Einstein-Hilbert action and a positive cosmological constant in its spontaneously broken phase. A more fundamental Weyl-Dirac-Born-Infeld gauge theory action exists in Weyl geometry, that does not need a UV regularisation, of which the (geometrically regularised) Weyl gauge theory is the leading order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07508 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The fall and the rise of Weyl gauge theory Ghilencea, D. M. General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of a spacetime symmetry, the Weyl gauge theory (of dilatations and Poincaré symmetry). The initial physical interpretation of his theory was however short-lived and led to the downfall of Weyl geometry as a physical theory. We review how this action was re-born into a physical Weyl gauge theory of gravity. This is the only gauge theory of a spacetime symmetry with a physical gauge boson, is Weyl anomaly-free, has {\it exact} geometric interpretation, with all scales of geometric origin, and generates Einstein-Hilbert action and a positive cosmological constant in its spontaneously broken phase. A more fundamental Weyl-Dirac-Born-Infeld gauge theory action exists in Weyl geometry, that does not need a UV regularisation, of which the (geometrically regularised) Weyl gauge theory is the leading order. |
| title | The fall and the rise of Weyl gauge theory |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.07508 |