Structure of Carrollian (conformal) superalgebra
Abstract In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both d = 4 and d = 3. For the super-Carrollian algebra in d = 4, we identify multiple admissible structures, depending on the representations of the supercharges...
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| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2025)111 |
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| author | Yu-fan Zheng Bin Chen |
| author_facet | Yu-fan Zheng Bin Chen |
| author_sort | Yu-fan Zheng |
| collection | DOAJ |
| description | Abstract In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both d = 4 and d = 3. For the super-Carrollian algebra in d = 4, we identify multiple admissible structures, depending on the representations of the supercharges with respect to the Carrollian rotation. Some of these structures can be derived by taking the speed of light c → 0 limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we derive nontrivial Carrollian superconformal algebras in dimensions d = 4 and d = 3. Among these, the superconformal algebra in d = 4 and one of the algebras in d = 3 exhibit isomorphisms to the super-Poincaré algebras in d = 5 and d = 4, respectively. Additionally, we identify a novel, nontrivial superconformal algebra in d = 3 that is not isomorphic to any super-Poincaré algebra. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Given that BMS4 algebra constitutes the infinite-dimensional extension of the d = 3 Carrollian conformal algebra, their supersymmetric extension gives rise to nontrivial superconformal Carrollian algebras. Specifically, we demonstrate the existence of a singlet super-BMS4 algebra emerging from the extension of the d = 3 Carrollian superconformal algebra, as well as a multiplet super-BMS4 algebra that does not admit this methodology, as its finite-dimensional subalgebra incorporates supercharges with conformal dimension ∆ = ± 3 2 $$ \frac{3}{2} $$ . |
| format | Article |
| id | doaj-art-c5b3eda5f5274ff7ae09d327b3707e0a |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-c5b3eda5f5274ff7ae09d327b3707e0a2025-08-20T03:42:26ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025813110.1007/JHEP08(2025)111Structure of Carrollian (conformal) superalgebraYu-fan Zheng0Bin Chen1Beijing Institute of Mathematical Sciences and Applications (BIMSA)Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo UniversityAbstract In this work, we investigate possible supersymmetric extensions of the Carrollian algebra and the Carrollian conformal algebra in both d = 4 and d = 3. For the super-Carrollian algebra in d = 4, we identify multiple admissible structures, depending on the representations of the supercharges with respect to the Carrollian rotation. Some of these structures can be derived by taking the speed of light c → 0 limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we derive nontrivial Carrollian superconformal algebras in dimensions d = 4 and d = 3. Among these, the superconformal algebra in d = 4 and one of the algebras in d = 3 exhibit isomorphisms to the super-Poincaré algebras in d = 5 and d = 4, respectively. Additionally, we identify a novel, nontrivial superconformal algebra in d = 3 that is not isomorphic to any super-Poincaré algebra. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Given that BMS4 algebra constitutes the infinite-dimensional extension of the d = 3 Carrollian conformal algebra, their supersymmetric extension gives rise to nontrivial superconformal Carrollian algebras. Specifically, we demonstrate the existence of a singlet super-BMS4 algebra emerging from the extension of the d = 3 Carrollian superconformal algebra, as well as a multiplet super-BMS4 algebra that does not admit this methodology, as its finite-dimensional subalgebra incorporates supercharges with conformal dimension ∆ = ± 3 2 $$ \frac{3}{2} $$ .https://doi.org/10.1007/JHEP08(2025)111AdS-CFT CorrespondenceScale and Conformal SymmetriesSupersymmetry and Duality |
| spellingShingle | Yu-fan Zheng Bin Chen Structure of Carrollian (conformal) superalgebra Journal of High Energy Physics AdS-CFT Correspondence Scale and Conformal Symmetries Supersymmetry and Duality |
| title | Structure of Carrollian (conformal) superalgebra |
| title_full | Structure of Carrollian (conformal) superalgebra |
| title_fullStr | Structure of Carrollian (conformal) superalgebra |
| title_full_unstemmed | Structure of Carrollian (conformal) superalgebra |
| title_short | Structure of Carrollian (conformal) superalgebra |
| title_sort | structure of carrollian conformal superalgebra |
| topic | AdS-CFT Correspondence Scale and Conformal Symmetries Supersymmetry and Duality |
| url | https://doi.org/10.1007/JHEP08(2025)111 |
| work_keys_str_mv | AT yufanzheng structureofcarrollianconformalsuperalgebra AT binchen structureofcarrollianconformalsuperalgebra |