Higher Spins from Tensorial Charges and OSp(N|2n) Symmetry

TL;DR

The paper demonstrates that quantizing a superparticle in a flat tensorial $N=1, D=4$ superspace produces an infinite tower of massless higher-spin states that satisfy Vasiliev's unfolded equations, with a parallel construction on the AdS$_4$ background using the supergroup manifold $OSp(1|4)$. A central technical advance is the discovery of $GL(2n)$-flat Cartan forms for $OSp(1|2n)$, which enables a tractable quantization on both flat and AdS$_4$ tensorial superspaces and clarifies the link to unfolded higher-spin dynamics. The work unifies twistor techniques, coset realizations, and the unfolded formalism by showing how the quantum spectrum of a tensorial superparticle maps onto the hierarchy of free higher-spin fields, and it extends to a minimal $N=1$ supersymmetric higher-spin theory on $AdS_4$ with potential implications for broader supergroup structures in fundamental theory.

Abstract

It is shown that the quantization of a superparticle propagating in an N=1, D=4 superspace extended with tensorial coordinates results in an infinite tower of massless spin states satisfying the Vasiliev unfolded equations for free higher spin fields in flat and AdS_4 N=1 superspace. The tensorial extension of the AdS_4 superspace is proved to be a supergroup manifold OSp(1|4). The model is manifestly invariant under an OSp(N|8) (N=1,2) superconformal symmetry. As a byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n) groups are GL(2n) flat, i.e. they are equivalent to flat Cartan forms up to a GL(2n) rotation. This property is crucial for carrying out the quantization of the particle model on OSp(1|4) and getting the higher spin field dynamics in super AdS_4, which can be performed in a way analogous to the flat case.