Higher-derivative superparticle in AdS$_3$ space

TL;DR

This paper constructs supersymmetric superparticle actions in AdS3 space, including higher-derivative terms, and explores their nonrelativistic limits, revealing how supersymmetry constrains these complex models.

Contribution

It introduces a coset approach to formulating superparticle actions with higher derivatives in AdS3, extending to nonrelativistic Newton-Hooke cases with fixed structures by supersymmetry.

Findings

Component actions are simplified using covariant Cartan forms.

Higher-derivative superparticle actions are explicitly constructed.

Nonrelativistic limits lead to Newton-Hooke superparticles with fixed structures.

Abstract

Employing the coset approach we construct component actions for a superparticle moving in AdS$_3$ with $N{=}(2,0)$, $D{=}3$ supersymmetry partially broken to $N{=}2$, $d{=}1$. These actions may contain higher time-derivative terms, which are chosen to possess the same (super)symmetries as the free superparticle. In terms of the nonlinear-realization superfields, the component actions always take a simpler form when written in terms of covariant Cartan forms. We also consider in detail the reduction to the nonrelativistic case and construct the corresponding action a Newton-Hooke superparticle and its higher-derivative generalizations. The structure of these higher time-derivative generalizations is completely fixed by invariance under the supersymmetric Newton-Hooke algebra extended by two central charges.