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arXiv · hep-th/9201020

The Superparticle and the Lorentz Group

A. S. Galperin·K. S. Stelle
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Abstract

We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $κ$-symmetry for worldline supersymmetry. We show that these twistor-like variables naturally parametrise the coset space ${\cal G}/{\cal H}$, where $\cal G$ is the Lorentz group $SO^\uparrow(1,d-1)$ and $\cal H$ is its maximal subgroup. This space is a compact manifold, the sphere $S^{d-2}$. Our group-theoretical construction gives the proper covariantisation of a fixed light-cone frame and clarifies the relation between target-space and worldline supersymmetries.

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A. S. Galperin, K. S. Stelle. 1992-01-11. The Superparticle and the Lorentz Group. https://doi.org/10.1016/0550-3213(92)90527-i

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