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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2025)111 |
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| Summary: | 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 $$ \frac{3}{2} $$ . |
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| ISSN: | 1029-8479 |