Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-12-30
Mod.Phys.Lett.A21:2117-2132,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, 13 pages, no figures; Talk at the Conference ``Cosmology 2005: a reality check'', December 14-17, 2005, Copenhagen, Den
Scientific paper
10.1142/S0217732306021517
Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor $\lambda_{a}$ and Ramond grassmannian vector $\psi_{m}=-{1\over 2}(\bar\theta\gamma_{m}\lambda)$ in the spinor realization \cite{VZ} are proposed. The map of supergravity background into composite supercoordinates: $(B^{-1}_{mn}, \Psi^{a}_{m}, C_{ab}) \leftrightarrow (i\psi_{m}\psi_{n}, \psi_{m}\lambda^{a}, \lambda_{a}\lambda_{b})$ valid up to the second order corrections in deformation parameter $h$ and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector $\psi_{1m}={1/2}(\bar\theta\gamma_{m}\gamma_{5}\lambda)$ and to vanish for the $\theta$ components with the same chiralities. The deformations in the (super)twistor picture are discussed.
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