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

Abstract

A supersymmetric Lorentz invariant mechanism for superspace deformations is proposed. It is based on an extension of superspace by one ${\lambda }_a$ 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: ${\theta }_{mn}\leftrightarrow i{\psi }_m{\psi }_n,C_{ab}\leftrightarrow {\lambda }_a{\lambda }_b,{\Psi }_m^a\leftrightarrow {\psi }_m{\lambda }^a$ 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 ${\psi }_m=-\frac{1}{2}(\bar{\theta }{\gamma }_m\lambda )$ as a covariant measure of space-time coordinate noncommutativity.

Latex, 16 pages; references added, typos corrected

Cited by in corpus (2)

• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Nilpotent noncommutativity and renormalization