Effective field theories as Lagrange spaces
Abstract We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariant...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2023)069 |
| _version_ | 1797199654659555328 |
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| author | Nathaniel Craig Yu-Tse Lee Xiaochuan Lu Dave Sutherland |
| author_facet | Nathaniel Craig Yu-Tse Lee Xiaochuan Lu Dave Sutherland |
| author_sort | Nathaniel Craig |
| collection | DOAJ |
| description | Abstract We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry. |
| first_indexed | 2024-03-08T10:17:25Z |
| format | Article |
| id | doaj.art-128f55ba55454e72b125597c81b81595 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T07:19:12Z |
| publishDate | 2023-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-128f55ba55454e72b125597c81b815952024-04-21T11:05:36ZengSpringerOpenJournal of High Energy Physics1029-84792023-11-0120231113510.1007/JHEP11(2023)069Effective field theories as Lagrange spacesNathaniel Craig0Yu-Tse Lee1Xiaochuan Lu2Dave Sutherland3Department of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaSchool of Physics and Astronomy, University of GlasgowAbstract We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry.https://doi.org/10.1007/JHEP11(2023)069Effective Field TheoriesDifferential and Algebraic GeometrySMEFT |
| spellingShingle | Nathaniel Craig Yu-Tse Lee Xiaochuan Lu Dave Sutherland Effective field theories as Lagrange spaces Journal of High Energy Physics Effective Field Theories Differential and Algebraic Geometry SMEFT |
| title | Effective field theories as Lagrange spaces |
| title_full | Effective field theories as Lagrange spaces |
| title_fullStr | Effective field theories as Lagrange spaces |
| title_full_unstemmed | Effective field theories as Lagrange spaces |
| title_short | Effective field theories as Lagrange spaces |
| title_sort | effective field theories as lagrange spaces |
| topic | Effective Field Theories Differential and Algebraic Geometry SMEFT |
| url | https://doi.org/10.1007/JHEP11(2023)069 |
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