Preprint 15/1998

Lorentz covariant spin two superspaces

Chandrashekar Devchand and Jean Nuyts

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Submission date: 08. Apr. 1998
Pages: 22
published in: Nuclear physics / B, 527 (1998) 3, p. 479-498 
DOI number (of the published article): 10.1016/S0550-3213(98)00433-7
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Superalgebras including generators having spins up to two and realisable as tangent vector fields on Lorentz covariant generalised superspaces are considered. The latter have a representation content reminiscent of configuration spaces of (super)gravity theories. The most general canonical supercommutation relations for the corresponding phase space coordinates allowed by Lorentz covariance are discussed. By including generators transforming according to every Lorentz representation having spin up to two, we obtain, from the super Jacobi identities, the complete set of quadratic equations for the Lorentz covariant structure constants. These defining equations for spin two Heisenberg superalgebras are highly overdetermined. Nevertheless, non-trivial solutions can indeed be found. By making some simplifying assumptions, we explicitly construct several classes of these superalgebras. E-Appendix: Defining equations for spin two superalgebras

The general structure equations for spin two superalgebras are archived here.

The super Jacobi identities require the vanishing of these 7725 quadratic polynomials

(163 tuc-equations,

1993 tt-equations,

5569 tu-equations)

in the 517 parameters (structure constants) consisting of the 15 c`s and

the 196 t`s + 339 u`s.

18.10.2019, 02:10