A Simple Particle Action from a Twistor Parametrization of AdS_5

TL;DR

This paper extends twistor theory to AdS_5, enabling a simple particle action formulation that could lead to new insights into string dynamics in this space.

Contribution

It introduces a novel twistor parametrization for AdS_5, including the radial coordinate, simplifying the particle action and potentially aiding string theory formulations.

Findings

Linear realization of SO(4,2) on twistors induces AdS_5 isometries

Particle action reduces to a 1D gauge theory in twistor variables

Potential for a simple string worldvolume action in AdS_5

Abstract

The SO(4,2) isometries of AdS_5 are realized non-linearly on its horospherical coordinates (x^m,\rho). On the other hand, Penrose twistors have long been known to linearly realize these symmetries on 4-dimensional Minkowski space, the boundary of AdS_5, parametrized by x^m. Here we extend the twistor construction and define a pair of twistors, allowing us to include a radial coordinate in the construction. The linear action of SO(4,2) on the twistors induces the correct isometries of AdS_5. We apply this new construction to the study of the dynamics of a massive particle in AdS_5. We show that in terms of the twistor variables the action takes a simple form of a 1-dimensional gauge theory. Our result might open up the possibility to find a simple worldvolume action also for the string propagating on AdS_5.