Abstract
The supertwistor and bi-supertwistor formulations for \( \mathcal{N} \)-extended anti-de Sitter (AdS) superspace in four dimensions, \( Ad{S}^{4\mid 4\mathcal{N}} \), were derived two years ago in [1]. In the present paper, we introduce a novel realisation of the \( \mathcal{N} \)-extended AdS supergroup OSp(\( \mathcal{N} \)|4; ℝ) and apply it to develop a coset construction for \( {\textrm{AdS}}^{4\mid 4\mathcal{N}} \) and the corresponding differential geometry. This realisation naturally leads to an atlas on \( {\textrm{AdS}}^{4\mid 4\mathcal{N}} \) (that is a generalisation of the stereographic projection for a sphere) that consists of two charts with chiral transition functions for \( \mathcal{N} \) > 0. A manifestly OSp(\( \mathcal{N} \)|4; ℝ) invariant model for a superparticle in \( {\textrm{AdS}}^{4\mid 4\mathcal{N}} \) is proposed. Additionally, by employing a conformal superspace approach, we describe the most general conformally flat \( \mathcal{N} \)-extended supergeometry. This construction is then specialised to the case of \( {\textrm{AdS}}^{4\mid 4\mathcal{N}} \).
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Acknowledgments
We are grateful to Alex Arvanitakis, Dmitri Sorokin and Gabriele Tartaglino-Mazzucchelli for discussions. SMK is grateful to the organisers of the CQUeST-APCTP Workshop “Gravity beyond Riemannian Paradigm” (Jeju Island, South Korea) where part of this work was completed, for the fantastic scientific atmosphere and generous support. He also acknowledges kind hospitality and generous support extended to him during his research stay at KIAS, Seoul. The work of SMK and ESNR is supported in part by the Australian Research Council, projects DP200101944 and DP230101629. The work of NEK is supported by the Australian Government Research Training Program Scholarship.
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Koning, N.E., Kuzenko, S.M. & Raptakis, E.S.N. Embedding formalism for \( \mathcal{N} \)-extended AdS superspace in four dimensions. J. High Energ. Phys. 2023, 63 (2023). https://doi.org/10.1007/JHEP11(2023)063
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DOI: https://doi.org/10.1007/JHEP11(2023)063