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

TL;DR

This paper demonstrates that quantizing a superparticle in extended superspace yields an infinite spectrum of massless higher spin fields satisfying Vasiliev's equations, with the model exhibiting superconformal symmetry and flatness properties of certain group forms.

Contribution

It introduces a superparticle model in tensorial superspace that produces higher spin fields and reveals the flatness of Cartan forms in Sp(2n) and OSp(1|2n) groups, facilitating higher spin dynamics in super AdS_4.

Findings

Infinite tower of massless higher spin states obtained.

Superconformal invariance under OSp(N|8) established.

Cartan forms of Sp(2n) and OSp(1|2n) are GL(2n) flat.

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.