The $AdS$ particle

TL;DR

This paper explores a relativistic particle model in AdS space, deriving Snyder algebra and kappa-Minkowski spacetime, and discusses the challenges of constructing noncommutative spacetime in open string theory.

Contribution

It introduces a Nambu-Goto model in AdS space that recovers the exotic oscillator and derives related noncommutative geometries.

Findings

Recovered the exotic oscillator from the AdS particle model

Derived Snyder algebra and kappa-Minkowski spacetime

Commented on the limitations of noncommutative spacetime in open string theory

Abstract

In this note we have considered a relativistic Nambu-Goto model for a particle in $AdS$ metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed \cite{pal} "Exotic Oscillator". The Snyder algebra and subsequently the $\kappa$-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncommutative spacetime in the context of open string where only a curved target space is introduced.