The anti-de Sitter supergeometry revisited
Year: 2025
Type: article
Abstract: A bstract In a supergravity framework, the $$ \mathcal{N} $$ N -extended anti-de Sitter (AdS) superspace in four spacetime dimensions, $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N , is a maximally symmetric background that is described by a curved superspace geometry with structure group SL(2, ℂ ) × $$ \textrm{U}\left(\mathcal{N}\right) $$ U N . On the other hand, within the group-theoretic setting, $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N is realised as the coset superspace $$ \textrm{O}\textrm{Sp}\left(\left.\mathcal{N}\right|4;\mathbb{R}\right)/\left[\textrm{SL}\left(2,\mathbb{C}\right)\times \textrm{O}\left(\mathcal{N}\right)\right] $$ OSp N 4 ℝ / SL 2 ℂ × O N , with its structure group being SL(2, ℂ ) × $$ \textrm{O}\left(\mathcal{N}\right) $$ O N . Here we explain how the two frameworks are related. We give two explicit realisations of $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N as a conformally flat superspace, thus extending the $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 results available in the literature. As applications, we describe: (i) a two-parameter deformation of the $$ {\textrm{AdS}}^{4\left|4\mathcal{N}\right.} $$ AdS 4 4 N interval and the corresponding superparticle model; (ii) some implications of conformal flatness for superconformal higher-spin multiplets and an effective action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly; and (iii) κ -symmetry of the massless AdS superparticle.
Source: Journal of High Energy Physics
Institution: The University of Western Australia
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408044574