Anti-de Sitter particles and manifest (super)isometries

TL;DR

This paper explores the classical and quantum properties of particles in anti-de Sitter spacetime, deriving bounds, formulating actions with manifest symmetries, and extending results to superparticles and null strings.

Contribution

It introduces a bi-twistor action formulation with linearly realized isometries and extends the analysis to superparticles and null strings in AdS backgrounds.

Findings

Recovered the Breitenlohner-Freedman bound via quantization.

Formulated a bi-twistor action with linearly realized AdS isometries for specific dimensions.

Quantization of superparticles yields a 128+128 supermultiplet.

Abstract

Starting from the classical action for a spin-zero particle in a D-dimensional anti-Sitter (AdS) spacetime, we recover the Breitenlohner-Freedman bound by quantization. For D=4,5,7, and using an Sl(2;K) spinor notation for K=R,C,H, we find a bi-twistor form of the action for which the AdS isometry group is linearly realised, although only for zero mass when D=4,7, in agreement with previous constructions. For zero mass and D=4, the conformal isometry group is linearly realized. We extend these results to the superparticle in the maximally supersymmetric "AdS x S" string/M-theory vacua, showing that quantization yields a 128+128 component supermultiplet. We also extend them to the null string.