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Vector supersymmetry: Casimir operators and contraction from Ø\(S\)p(3,2 |2). (English) Zbl 1243.81085

Summary: We study some algebraic properties of the ‘vector supersymmetry’ (VSUSY) algebra, a graded extension of the four-dimensional Poincar{é 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.}

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
17B81 Applications of Lie (super)algebras to physics, etc.
81Q60 Supersymmetry and quantum mechanics
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