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

References in corpus (31)

• Superbranes and Superembeddings
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• N=1 Conformal Superspace in Four Dimensions
• 4D N = 2 Supergravity and Projective Superspace
• Superconformal Symmetry and Correlation Functions
• On conformal supergravity and projective superspace
• N=2 Conformal Superspace in Four Dimensions
• On compactified harmonic/projective superspace, 5D superconformal theories, and all that
• Field theory in 4D N=2 conformally flat superspace
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Supertwistors as Quarks of SU(2,2|4)
• OSp supergroup manifolds, superparticles and supertwistors
• On the Superconformal Flatness of AdS Superspaces
• Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics
• N=2 AdS supergravity and supercurrents
• A dual formulation of supergravity-matter theories
• Twistor methods for AdS${}_5$
• Conformally compactified Minkowski superspaces revisited
• A Simple Particle Action from a Twistor Parametrization of AdS_5
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• Anti-de Sitter particles and manifest (super)isometries
• Superconformal geometries and local twistors
• Symmetries of supergravity backgrounds and supersymmetric field theory
• BRST Quantization of a Particle in AdS_5
• Geometric Construction of AdS Twistors
• AdS twistors for higher spin theory
• Supertwistor formulation for massless superparticle in $Ad{S}_5\times S^5$ superspace
• Twistor description of spinning particles in AdS
• Superconformal structures on the three-sphere
• Twistors and Actions on Coset Manifolds
• Embedding formalism for $(p,q)$ AdS superspaces in three dimensions

Cited by in corpus (1)

• The anti-de Sitter supergeometry revisited