Superspace Formulation of 4D Higher Spin Gauge Theory

TL;DR

This work develops a minimal ${\cal N}=1$ superspace formulation for 4D AdS HS gauge theory based on the hs$(1|4)$ algebra, keeping the internal twistor space while replacing spacetime with ${\cal N}=1$ superspace. The authors define master fields $\\widehat{A}$ and $\\widehat{\\Phi}$ subject to integrable curvature constraints, and show that projecting to ordinary superspace recovers the known spacetime HS equations, with a curvature expansion solving for the $Z$-dependence. They demonstrate that the ${\cal R}$-constraint encodes the on-shell ${\cal N}=1$ supergravity multiplet (with cosmological constant) and that the ${\cal F}^{(1)}$-constraint yields the HS field-strength equations, while the $\\Phi$-constraint isolates the physical scalar multiplet at level $(-1,1/2)$, all within a consistent level-by-level decomposition. The formalism generalizes to ${\cal N}\ge 2$ HS theories and to higher dimensions (e.g., ${\cal N}=4$, $D=5$ with hs$(2,2|4)$), offering a manifestly supersymmetric, diffeomorphism-invariant framework for HS interactions and potential couplings to extended objects in AdS backgrounds.

Abstract

Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory in superspace, leaving the internal twistor space intact. Remarkably, the superspace constraints have the same form as those defining the theory in ordinary spacetime. This construction generalizes straightforwardly to higher spin gauge theories N>1 supersymmetry.