Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions

Abstract

The supertwistor and bi-supertwistor formulations for $\mathcal{N}$-extended anti-de Sitter (AdS) superspace in four dimensions, ${\mathrm{AdS}}^{4|4\mathcal{N}}$, were derived two years ago in arXiv:2108.03907. In the present paper, we introduce a novel realisation of the $\mathcal{N}$-extended AdS supergroup $\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$ and apply it to develop a coset construction for ${\mathrm{AdS}}^{4|4\mathcal{N}}$ and the corresponding differential geometry. This realisation naturally leads to an atlas on ${\mathrm{AdS}}^{4|4\mathcal{N}}$ (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 $\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$ invariant model for a superparticle in ${\mathrm{AdS}}^{4|4\mathcal{N}}$ 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 ${\mathrm{AdS}}^{4|4\mathcal{N}}$.

50 pages; v2: published version; v3: comments in section 6.4 added and error in eq. (6.42) corrected; v4: typo corrected