Minimal realization of ℓ-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

Abstract

We present the minimal realization of the ℓ-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex PaisUhlenbeck oscillator equations. We introduce a minimal deformation of the ℓ = 1/2 conformal Galilei (a.k.a. Schrödinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d = 1 conformal group, we find a massive extension of the near-horizon Kerr-dS/AdS metric.