The Superparticle and the Lorentz Group

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 $\kappa$-symmetry for worldline supersymmetry. We show that these twistor-like variables naturally parametrise the coset space $\mathcal{G}/\mathcal{H}$, where $\mathcal{G}$ is the Lorentz group $S{O}^{\uparrow }(1,d-1)$ and $\mathcal{H}$ 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.

33 pages