SU(2|2) supersymmetric mechanics

Abstract

We introduce a new kind of non-relativistic $\mathcal{N}=8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat $\mathcal{N}=8$, $d=1$ supersymmetry. Various worldline $SU(2|2)$ superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell $SU(2|2)$ multiplets $(3,8,5)$, $(4,8,4)$ and $(5,8,3)$, we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group $OSp(4^{\ast }|4)$ in the conformal cases. For the simplest $(5,8,3)$ model the quantization is performed.

1+36 pages; v2: comments and ref.[49] added, typos corrected, matches published version

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• On the spectrum-generating superalgebras of the deformed one-dimensional quantum oscillators
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Superfield approach to higher derivative N=1 superconformal mechanics
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• Supersymmetric Calogero models from superfield gauging
• Superintegrable deformations of oscillator and Coulomb systems