Abstract
Within the framework of $$ \mathcal{N} $$
N
= 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$
V
α
m
α
⋅
n
≔
V
α
1
…
αm
α
⋅
1
…
α
⋅
n
on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$
V
α
m
α
⋅
n
into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$
N
= 1 AdS4 superalgebra $$ \mathfrak{osp} $$
osp
(1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.
Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient