Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential
Abstract We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ( R ˜ $$ \tilde{R} $$ ) and in the Weyl tensor ( C ˜ μνρσ $$ {\tilde{C}}_{\mu \nu \rho \sigma} $$ ) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2019)049 |
| _version_ | 1819062388255621120 |
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| author | D. M. Ghilencea |
| author_facet | D. M. Ghilencea |
| author_sort | D. M. Ghilencea |
| collection | DOAJ |
| description | Abstract We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ( R ˜ $$ \tilde{R} $$ ) and in the Weyl tensor ( C ˜ μνρσ $$ {\tilde{C}}_{\mu \nu \rho \sigma} $$ ) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field ω μ becomes massive (mass m ω ∼ Planck scale) after “eating” the dilaton in the R ˜ $$ \tilde{R} $$ 2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field ω μ . Below m ω this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a “low-energy” limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field ϕ 1 (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling ξ 1 ϕ 1 2 R ˜ $$ {\xi}_1{\phi}_1^2\tilde{R} $$ to Weyl geometry, with Higgs mass ∝ ξ1/ξ0 (ξ0 is the coefficient of the R ˜ $$ \tilde{R} $$ 2 term). In realistic models ξ1 must be classically tuned ξ1 ≪ ξ0. We comment on the quantum stability of this value. |
| first_indexed | 2024-12-21T14:57:59Z |
| format | Article |
| id | doaj.art-51c465ce28b44080bd4bfec7d8996345 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T14:57:59Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-51c465ce28b44080bd4bfec7d89963452022-12-21T18:59:42ZengSpringerOpenJournal of High Energy Physics1029-84792019-03-012019311510.1007/JHEP03(2019)049Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potentialD. M. Ghilencea0Department of Theoretical Physics, National Institute of Physics and Nuclear EngineeringAbstract We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ( R ˜ $$ \tilde{R} $$ ) and in the Weyl tensor ( C ˜ μνρσ $$ {\tilde{C}}_{\mu \nu \rho \sigma} $$ ) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field ω μ becomes massive (mass m ω ∼ Planck scale) after “eating” the dilaton in the R ˜ $$ \tilde{R} $$ 2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field ω μ . Below m ω this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a “low-energy” limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field ϕ 1 (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling ξ 1 ϕ 1 2 R ˜ $$ {\xi}_1{\phi}_1^2\tilde{R} $$ to Weyl geometry, with Higgs mass ∝ ξ1/ξ0 (ξ0 is the coefficient of the R ˜ $$ \tilde{R} $$ 2 term). In realistic models ξ1 must be classically tuned ξ1 ≪ ξ0. We comment on the quantum stability of this value.http://link.springer.com/article/10.1007/JHEP03(2019)049Classical Theories of GravityEffective Field TheoriesHiggs PhysicsSpontaneous Symmetry Breaking |
| spellingShingle | D. M. Ghilencea Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential Journal of High Energy Physics Classical Theories of Gravity Effective Field Theories Higgs Physics Spontaneous Symmetry Breaking |
| title | Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential |
| title_full | Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential |
| title_fullStr | Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential |
| title_full_unstemmed | Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential |
| title_short | Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential |
| title_sort | spontaneous breaking of weyl quadratic gravity to einstein action and higgs potential |
| topic | Classical Theories of Gravity Effective Field Theories Higgs Physics Spontaneous Symmetry Breaking |
| url | http://link.springer.com/article/10.1007/JHEP03(2019)049 |
| work_keys_str_mv | AT dmghilencea spontaneousbreakingofweylquadraticgravitytoeinsteinactionandhiggspotential |