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. This is a review of two different types of the deformed N = 4 and N = 8 supersymmetric mechanics. The first type is associated with the worldline realizations of the supergroups S U(2|1) (four supercharges), as well as of S U(2|2) and S U(4|1) (eight supercharges). The second type is the quaternionKähler (QK) deformation of the hyper-Kähler (HK) N = 4 mechanics models. The basic distinguishing feature of the QK models is a local N = 4 supersymmetry realized in d = 1 harmonic superspace.

New deformations of N = 4 and N = 8 supersymmetric mechanics