$\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace
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| Format: | Preprint |
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2025
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| _version_ | 1866917049873203200 |
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| author | Ivanov, Evgeny Zaigraev, Nikita |
| author_facet | Ivanov, Evgeny Zaigraev, Nikita |
| contents | We present the harmonic superspace formulation of $\mathcal{N}=2$ hypermultiplet in AdS$_4$ background, starting from the proper realization of $4D, \mathcal{N}=2$ superconformal group $SU(2,2|2)$ on the analytic subspace coordinates. The key observation is that $\mathcal{N}=2$ AdS$_4$ supergroup $OSp(2|4)$ can be embedded as a subgroup in the superconformal group through introducing a constant symmetric matrix $c^{(ij)}$ and identifying the AdS supercharge as $Ψ^i_α= Q^i_α+ c^{ik} S_{kα}$, with $Q$ and $S$ being generators of the standard and conformal $4D, {\cal N}=2$ supersymmetries. Respectively, the AdS cosmological constant is given by the square of $c^{(ij)}$, $Λ= -12 c^{ij}c_{ij}$. We construct the $OSp(2|4)$ invariant hypermultiplet mass term by adding, to the coordinate AdS transformations, a piece realized as an extra $SO(2)$ rotation of the hypermultiplet superfield. It is analogous to the central charge $x^5$ transformation of flat $\mathcal{N}=2$ supersymmetry and turns into the latter in the super Minkowski limit. As another new result, we explicitly construct the superfield Weyl transformation to the $OSp(2|4)$ invariant AdS integration measure over the analytic superspace, which provides, in particular, a basis for unconstrained superfield formulations of the AdS$_4$-deformed $\mathcal{N}=2$ hyper Kähler sigma models. We find the proper redefinition of $θ$ coordinates ensuring the AdS-covariant form of the analytic superfield component expansions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_01406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace Ivanov, Evgeny Zaigraev, Nikita High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We present the harmonic superspace formulation of $\mathcal{N}=2$ hypermultiplet in AdS$_4$ background, starting from the proper realization of $4D, \mathcal{N}=2$ superconformal group $SU(2,2|2)$ on the analytic subspace coordinates. The key observation is that $\mathcal{N}=2$ AdS$_4$ supergroup $OSp(2|4)$ can be embedded as a subgroup in the superconformal group through introducing a constant symmetric matrix $c^{(ij)}$ and identifying the AdS supercharge as $Ψ^i_α= Q^i_α+ c^{ik} S_{kα}$, with $Q$ and $S$ being generators of the standard and conformal $4D, {\cal N}=2$ supersymmetries. Respectively, the AdS cosmological constant is given by the square of $c^{(ij)}$, $Λ= -12 c^{ij}c_{ij}$. We construct the $OSp(2|4)$ invariant hypermultiplet mass term by adding, to the coordinate AdS transformations, a piece realized as an extra $SO(2)$ rotation of the hypermultiplet superfield. It is analogous to the central charge $x^5$ transformation of flat $\mathcal{N}=2$ supersymmetry and turns into the latter in the super Minkowski limit. As another new result, we explicitly construct the superfield Weyl transformation to the $OSp(2|4)$ invariant AdS integration measure over the analytic superspace, which provides, in particular, a basis for unconstrained superfield formulations of the AdS$_4$-deformed $\mathcal{N}=2$ hyper Kähler sigma models. We find the proper redefinition of $θ$ coordinates ensuring the AdS-covariant form of the analytic superfield component expansions. |
| title | $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2509.01406 |