Towards N $$ \mathcal{N} $$ = 2 superconformal higher-spin theory

Abstract

Abstract Three years ago, we proposed free off-shell models for N $$ \mathcal{N} $$ = 2 superconformal higher-spin multiplets in arbitrary conformally flat backgrounds, constructed conserved conformal higher-spin supercurrents for a massless hypermultiplet, and sketched the Noether procedure to generate its cubic couplings to the superconformal higher-spin multiplets. This paper is devoted to completing the Noether procedure. Specifically, we: (i) describe the unique off-shell primary extensions of the conformal higher-spin supercurrents; (ii) embed the off-shell superconformal prepotentials into primary unconstrained isotwistor multiplets; and (iii) present the unique gauge transformations of the hypermultiplet and the isotwistor prepotentials. An extension of the Noether procedure beyond the cubic level is also sketched, following the earlier N $$ \mathcal{N} $$ = 1 superconformal approach developed by the authors and Ponds in 2022. Our construction is based on making use of the polar hypermultiplet within the projective-superspace setting.

Keywords

• Extended Supersymmetry
• Higher Spin Gravity
• Scale and Conformal Symmetries
• Superspaces