N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions
Abstract We develop a superspace formulation for N $$ \mathcal{N} $$ = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives ∇ A = ∇ a ∇ α i ∇ i α ⋅...
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| Format: | Article |
| Idioma: | English |
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SpringerOpen
2024-03-01
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| Col·lecció: | Journal of High Energy Physics |
| Matèries: | |
| Accés en línia: | https://doi.org/10.1007/JHEP03(2024)026 |
| _version_ | 1827205624039997440 |
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| author | Sergei M. Kuzenko Emmanouil S. N. Raptakis |
| author_facet | Sergei M. Kuzenko Emmanouil S. N. Raptakis |
| author_sort | Sergei M. Kuzenko |
| collection | DOAJ |
| description | Abstract We develop a superspace formulation for N $$ \mathcal{N} $$ = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives ∇ A = ∇ a ∇ α i ∇ i α ⋅ $$ {\nabla}_A=\left({\nabla}_a,{\nabla}_{\alpha}^i,{\nabla}_i^{\overset{\cdot }{\alpha }}\right) $$ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor W α of dimension +1/2 and its conjugate. Associated with W α is its primary descendant B i j of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for N $$ \mathcal{N} $$ = 3 conformal supergravity. We describe the model for linearised N $$ \mathcal{N} $$ = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe N $$ \mathcal{N} $$ = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell N $$ \mathcal{N} $$ = 3 super Yang-Mills theory coupled to conformal supergravity. |
| first_indexed | 2024-04-25T01:09:27Z |
| format | Article |
| id | doaj.art-8323a04cf9a84a609cc93525b4536a00 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T12:11:14Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8323a04cf9a84a609cc93525b4536a002024-06-30T11:07:29ZengSpringerOpenJournal of High Energy Physics1029-84792024-03-012024312810.1007/JHEP03(2024)026N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensionsSergei M. Kuzenko0Emmanouil S. N. Raptakis1Department of Physics M013, The University of Western AustraliaDepartment of Physics M013, The University of Western AustraliaAbstract We develop a superspace formulation for N $$ \mathcal{N} $$ = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives ∇ A = ∇ a ∇ α i ∇ i α ⋅ $$ {\nabla}_A=\left({\nabla}_a,{\nabla}_{\alpha}^i,{\nabla}_i^{\overset{\cdot }{\alpha }}\right) $$ is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor W α of dimension +1/2 and its conjugate. Associated with W α is its primary descendant B i j of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for N $$ \mathcal{N} $$ = 3 conformal supergravity. We describe the model for linearised N $$ \mathcal{N} $$ = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe N $$ \mathcal{N} $$ = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell N $$ \mathcal{N} $$ = 3 super Yang-Mills theory coupled to conformal supergravity.https://doi.org/10.1007/JHEP03(2024)026Extended SupersymmetryScale and Conformal SymmetriesSupergravity ModelsSuperspaces |
| spellingShingle | Sergei M. Kuzenko Emmanouil S. N. Raptakis N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions Journal of High Energy Physics Extended Supersymmetry Scale and Conformal Symmetries Supergravity Models Superspaces |
| title | N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions |
| title_full | N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions |
| title_fullStr | N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions |
| title_full_unstemmed | N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions |
| title_short | N $$ \mathcal{N} $$ = 3 conformal superspace in four dimensions |
| title_sort | n mathcal n 3 conformal superspace in four dimensions |
| topic | Extended Supersymmetry Scale and Conformal Symmetries Supergravity Models Superspaces |
| url | https://doi.org/10.1007/JHEP03(2024)026 |
| work_keys_str_mv | AT sergeimkuzenko nmathcaln3conformalsuperspaceinfourdimensions AT emmanouilsnraptakis nmathcaln3conformalsuperspaceinfourdimensions |