Superconformal geometries and local twistors
Abstract Superconformal geometries in spacetime dimensions D = 3, 4, 5 and 6 are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2021)140 |
| _version_ | 1818956652799328256 |
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| author | P. S. Howe U. Lindström |
| author_facet | P. S. Howe U. Lindström |
| author_sort | P. S. Howe |
| collection | DOAJ |
| description | Abstract Superconformal geometries in spacetime dimensions D = 3, 4, 5 and 6 are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and S-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in D = 3, 4. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories. |
| first_indexed | 2024-12-20T10:57:22Z |
| format | Article |
| id | doaj.art-9d8b5a7aaa314ae9aa5dfea322a40895 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T10:57:22Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9d8b5a7aaa314ae9aa5dfea322a408952022-12-21T19:43:07ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021413110.1007/JHEP04(2021)140Superconformal geometries and local twistorsP. S. Howe0U. Lindström1Department of Mathematics, King’s College LondonDepartment of Physics, Faculty of Arts and Sciences, Middle East Technical UniversityAbstract Superconformal geometries in spacetime dimensions D = 3, 4, 5 and 6 are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and S-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in D = 3, 4. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories.https://doi.org/10.1007/JHEP04(2021)140Differential and Algebraic GeometrySupergravity ModelsSuperspaces |
| spellingShingle | P. S. Howe U. Lindström Superconformal geometries and local twistors Journal of High Energy Physics Differential and Algebraic Geometry Supergravity Models Superspaces |
| title | Superconformal geometries and local twistors |
| title_full | Superconformal geometries and local twistors |
| title_fullStr | Superconformal geometries and local twistors |
| title_full_unstemmed | Superconformal geometries and local twistors |
| title_short | Superconformal geometries and local twistors |
| title_sort | superconformal geometries and local twistors |
| topic | Differential and Algebraic Geometry Supergravity Models Superspaces |
| url | https://doi.org/10.1007/JHEP04(2021)140 |
| work_keys_str_mv | AT pshowe superconformalgeometriesandlocaltwistors AT ulindstrom superconformalgeometriesandlocaltwistors |