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Anti–de Sitter flag superspace

Nowar E. Koning ^* and Sergei M. Kuzenko ^†

Department of Physics M013, The University of Western Australia, 35 Stirling Highway, Perth W.A. 6009, Australia

^*Contact author: nowar.koning@research.uwa.edu.au
^†Contact author: sergei.kuzenko@uwa.edu.au

Phys. Rev. D 113, 065019 – Published 24 March, 2026

DOI: https://doi.org/10.1103/r56q-l5cx

Abstract

This work aims to develop a global formulation for $N = 2$ harmonic/projective anti–de Sitter (AdS) superspace ${AdS}^{4 | 8} \times S^{2} ≃ {AdS}^{4 | 8} \times C P^{1}$ that allows for a simple action of superconformal (and hence AdS isometry) transformations. First of all, we provide an alternative supertwistor description of the $N$ -extended AdS superspace in four dimensions, ${AdS}^{4 | 4 N}$ , which corresponds to a realization of the connected component ${O S p}_{0} (N | 4; R)$ of the AdS isometry supergroup as $S U (2, 2 | N) \cap O S p (N | 4; C)$ . The proposed realization yields the following properties: (i) ${AdS}^{4 | 4 N}$ is an open domain of the compactified $N$ -extended Minkowski superspace, ${\bar{M}}^{4 | 4 N}$ ; (ii) the infinitesimal $N$ -extended superconformal transformations naturally act on ${AdS}^{4 | 4 N}$ ; and (iii) the isometry transformations of ${AdS}^{4 | 4 N}$ are described by those superconformal transformations which obey a certain constraint. The obtained results for ${AdS}^{4 | 4 N}$ are then applied to develop a supertwistor formulation for an AdS flag superspace ${AdS}^{4 | 8} \times F_{1} (2)$ that we identify with the $N = 2$ harmonic/projective AdS superspace. This construction makes it possible to read off the superconformal and AdS isometry transformations acting on the analytic subspace of the harmonic superspace.

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Phys. Rev. D 113, 065019– Published 24 March, 2026

Vol. 113, Iss. 6 — 15 March 2026

Received 6 January 2026
Accepted 25 February 2026

DOI: https://doi.org/10.1103/r56q-l5cx

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Anti–de Sitter flag superspace

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