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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.22160 |
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| _version_ | 1866916930521137152 |
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| author | Zheng, Yu-fan Chen, Bin |
| author_facet | Zheng, Yu-fan Chen, Bin |
| contents | 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 $c\to 0$ limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we demonstrate that the nontrivial Carrollian superconformal algebras for $d=4$ and $d=3$ are isomorphic to super-Poincaré algebra of $d=5$ and $d=4$ respectively. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Furthermore, we discover two distinct classes of super-BMS$_4$ algebras, i.e. one singlet super-BMS$_4$ algebra and two multiplet chiral super-BMS$_4$ algebras. The singlet case arises from extending the $3$D Carrollian superconformal algebra, whereas the multiplet cases do not admit this pathology due to their finite-dimensional subalgebra containing supercharges with conformal dimension $Δ=\pm\frac{3}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure of Carrollian (conformal) superalgebra Zheng, Yu-fan Chen, Bin High Energy Physics - Theory 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 $c\to 0$ limit from super-Poincaré algebra, but others are completely novel. In the conformal case, we demonstrate that the nontrivial Carrollian superconformal algebras for $d=4$ and $d=3$ are isomorphic to super-Poincaré algebra of $d=5$ and $d=4$ respectively. Remarkably, neither of these constructions requires R-symmetry to ensure the algebraic closure. Furthermore, we discover two distinct classes of super-BMS$_4$ algebras, i.e. one singlet super-BMS$_4$ algebra and two multiplet chiral super-BMS$_4$ algebras. The singlet case arises from extending the $3$D Carrollian superconformal algebra, whereas the multiplet cases do not admit this pathology due to their finite-dimensional subalgebra containing supercharges with conformal dimension $Δ=\pm\frac{3}{2}$. |
| title | Structure of Carrollian (conformal) superalgebra |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.22160 |