Continuous spin superparticle in $4D$, ${\cal N}=1$ curved superspace

TL;DR

This paper introduces a new model for a continuous spin superparticle in 4D AdS superspace, extending previous flat space models and analyzing the constraint structure and supergeometry restrictions.

Contribution

It generalizes the flat space continuous spin superparticle model to AdS superspace and clarifies the constraint classification and supergeometry conditions.

Findings

The model is consistent only in AdS supergeometry.

Bosonic constraints are all first-class.

Fermionic constraints split into one first-class and three second-class constraints.

Abstract

We present a new particle model that describes the dynamics of a $4D,$ $\mathcal{N}{=}\,1$ continuous spin particle in $AdS_4$ superspace and is a generalization of the continuous-spin superparticle model in flat $4D$, $\mathcal{N}{=}\,1$ superspace proposed in 2506.19709 [hep-th]. The model is described by $4D$, $\mathcal{N}{=}\,1$ superspace coordinates together with commuting spinor additional variables, which are inherent ingredients of continuous spin models. The Lagrangian and the system of four bosonic and four fermionic phase space constraints are derived. The consistency condition for constraints imposes a restriction on supergeometry to be $AdS$ superpace. It is shown that the bosonic constraints are first-class constraints. A covariant procedure based on the use of additional variables is developed to divide the four fermionic constraints into first and second classes. It is proved that, unlike the flat case, only one fermionic constraint is a first-class constraint, while the other three are second-class constraints. In the flat limit, one of these second-class constraints becomes a first-class one.