Embedding formalism for AdS superspaces in five dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916641639497728 |
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| author | Koning, Nowar E. Kuzenko, Sergei M. |
| author_facet | Koning, Nowar E. Kuzenko, Sergei M. |
| contents | The standard geometric description of $d$-dimensional anti-de Sitter (AdS) space is a quadric in ${\mathbb R}^{d-1,2}$ defined by $(X^0)^2 - (X^1)^2 - \dots - (X^{d-1})^2 + (X^d)^2 = \ell^2 = \text{const}$. In this paper we provide a supersymmetric generalisation of this embedding construction in the $d=5$ case. Specifically, a bi-supertwistor realisation is given for the ${\cal N}$-extended AdS superspace $\text{AdS}^{5|8\cal N}$, with ${\cal N}\geq 1$. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in $\text{AdS}^{5|8\cal N}$ which is manifestly invariant under the AdS isometry supergroup $\mathsf{SU}(2,2|{\cal N})$ and involves two independent two-derivative terms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_10875 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding formalism for AdS superspaces in five dimensions Koning, Nowar E. Kuzenko, Sergei M. High Energy Physics - Theory Mathematical Physics The standard geometric description of $d$-dimensional anti-de Sitter (AdS) space is a quadric in ${\mathbb R}^{d-1,2}$ defined by $(X^0)^2 - (X^1)^2 - \dots - (X^{d-1})^2 + (X^d)^2 = \ell^2 = \text{const}$. In this paper we provide a supersymmetric generalisation of this embedding construction in the $d=5$ case. Specifically, a bi-supertwistor realisation is given for the ${\cal N}$-extended AdS superspace $\text{AdS}^{5|8\cal N}$, with ${\cal N}\geq 1$. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in $\text{AdS}^{5|8\cal N}$ which is manifestly invariant under the AdS isometry supergroup $\mathsf{SU}(2,2|{\cal N})$ and involves two independent two-derivative terms. |
| title | Embedding formalism for AdS superspaces in five dimensions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2406.10875 |