Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

Abstract

We present the minimal realization of the $\ell$-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the $\ell$=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.

arXiv comment1+12 pages, v2: misprints corrected, 5 refs. added, including on the odd series of PU oscillators, published version

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• Schrödinger symmetry: a historical review
• Geometry of the isotropic oscillator driven by the conformal mode
• Meta-Schrödinger invariance
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Superfield approach to higher derivative N=1 superconformal mechanics
• SU(1,2) invariance in two-dimensional oscillator
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Oscillators from nonlinear realizations
• Remarks on Galilean electromagnetism