Supersymmetric Lorentz invariant deformations of superspaces

TL;DR

This paper introduces Lorentz invariant supersymmetric deformations of superspaces using a Moyal star product, mapping supergravity backgrounds into composite supercoordinates, and explores their properties and implications in twistor space.

Contribution

It proposes a new class of Lorentz invariant supersymmetric deformations of superspaces based on a Moyal star product, including a background map and analysis of their properties.

Findings

Deformations depend on an axial vector and vanish for same-chirality components.

The background map relates supergravity fields to composite supercoordinates.

Deformations can be expressed in the (super)twistor framework.

Abstract

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.