Vector Supersymmetry: Casimir operators and contraction from OSp(3,2|2)

Understand

We study some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra, a graded extension of the four-dimensional Poincare' algebra with two odd generators, a vector and a scalar, and two central charges.

• The anticommutator between the two odd generators gives the four-momentum operator, from which the name vector supersymmetry.
• We construct the Casimir operators for this algebra and we show how both algebra and Casimirs can be derived by contraction from the simple orthosymplectic algebra OSp(3,2|2).
• In particular, we construct the analogue of superspin for vector supersymmetry and we show that, due to the algebraic structure of the Casimirs, the multiplets are either doublets of spin (s,s+1) or two spin 1/2 states.