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Lorentz invariant supersymmetric mechanism for non(anti)commutative deformations of space-time geometry

A. A. Zheltukhin
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Abstract

A supersymmetric Lorentz invariant mechanism for superspace deformations is proposed. It is based on an extension of superspace by one $λ_{a}$ or several Majorana spinors associated with the Penrose twistor picture. Some examples of Lorentz invariant supersymmetric Poisson and Mojal brackets are constructed and the correspondence: $θ_{mn}\leftrightarrow iψ_{m}ψ_{n},\quad C_{ab}\leftrightarrow λ_{a}λ_{b},\quad Ψ^{a}_{m}\leftrightarrow ψ_{m}λ^{a}$ mapping the brackets depending on the constant background into the Lorentz covariant supersymmetric brackets is established. The correspondence reveals the role of the composite anticommuting vector $ψ_{m}=-{1\over 2}(\barθγ_{m}λ)$ as a covariant measure of space-time coordinate noncommutativity.

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A. A. Zheltukhin. 2005-06-19. Lorentz invariant supersymmetric mechanism for non(anti)commutative deformations of space-time geometry. https://arxiv.org/abs/hep-th/0506127

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