Vector Supersymmetry from OSp(3,2|2): Casimir Operators

TL;DR

This paper explores the algebraic structure of vector supersymmetry (VSUSY), deriving its Casimir operators, identifying spin-related operators, and showing its derivation from the OSp(3,2|2) superalgebra via contraction.

Contribution

It provides the first complete derivation of all Casimir operators for VSUSY and introduces a new spin operator, C-spin, within this algebraic framework.

Findings

Derived all independent Casimir operators of VSUSY.

Identified two spin-related operators, including a new C-spin fixed at 1/2.

Showed VSUSY can be obtained from OSp(3,2|2) via Inonu-Wigner contraction.

Abstract

In this paper we briefly review the main results obtained in arXiv:0812.1982, where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincare' algebra in 4 dimensions with two central charges. We derive all independent Casimir operators of VSUSY and we find two distinct spin-related operators in the case of nonvanishing central charges. One is the analogue of superspin for VSUSY and the other is a new spin, called C-spin, whose value is fixed to 1/2. We also show that the VSUSY algebra and its Casimir operators can be derived by an Inonu-Wigner contraction from OSp(3,2|2). This paper is based on the talk given in Varna, Bulgaria, during the 4-th EU RTN Workshop 2008.