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

TL;DR

This paper explores the algebraic structure of vector supersymmetry (VSUSY), constructs its Casimir operators, and shows how it can be derived from the orthosymplectic algebra OSp(3,2|2), revealing its representation properties.

Contribution

It introduces the algebraic properties of VSUSY, constructs its Casimir operators, and demonstrates their derivation from OSp(3,2|2) through contraction, including the analysis of multiplet structures.

Findings

Casimir operators for VSUSY are constructed.

VSUSY can be obtained by contraction from OSp(3,2|2).

Multiplets are either (s,s+1) doublets or two spin 1/2 states.

Abstract

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. Finally, we identify an odd operator, which is an invariant in a subclass of representations where a BPS-like algebraic relation between the mass and the values of the central charges is satisfied.