Abstract
The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D = 4, 5, 7, which linearises invariance under the AdS isometry group Sp(4; mathbb{K} ) for mathbb{K}=mathbb{R},mathbb{C},mathrm{mathbb{H}} , is generalized to the massless N -extended “spinning particle”. The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS5.
Highlights
A general feature of particle, string or brane dynamics is that isometries of the background spacetime become symmetries of the particle, string or brane action
There is no fundamental reason to exclude the worldline Chern-Simons (WCS) term, we show in the appendix that its inclusion creates a mismatch between the antide Sitter (AdS) isometry group and the manifest Sp(4; K) symmetry group of the action (7.1), so its inclusion in this context is problematic
This paper is the continuation of a previous one [21], inspired by results of Claus et al [7] and Cederwall [16, 17], on a two-twistor formulation of relativistic particle and superparticle mechanics in a D-dimensional anti-de Sitter background, for D = 4, 5, 7
Summary
A general feature of particle, string or brane dynamics is that isometries of the background spacetime become symmetries of the particle, string or brane action. An alternative is to exploit the fact that the AdSD isometry group is the conformal isometry group of its d-dimensional Minkowski boundary; twistor methods [3, 4] are available for some spacetime dimensions (as are supertwistor methods [5, 6]) This idea inspired a construction by Claus et al of an action for a massive spin-zero particle in AdS5 for which the AdS5 isometries are realized linearly on twistor variables [7]. A significant feature of that action (which carries over to the AdSD case) is that the twistor variables, and the new anticommuting variables required for non-zero spin, are all gauge invariant with respect to the original local worldline supersymmetry.
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