Quaternion-K\xe4hler mathcal{N} = 4 supersymmetric mechanics

Abstract

Using the mathcal{N} = 4, 1D harmonic superspace approach, we construct a new type of mathcal{N} = 4 supersymmetric mechanics involving 4n-dimensional Quaternion-Kähler (QK) 1D sigma models as the bosonic core. The basic ingredients of our construction are local mathcal{N} = 4,1D supersymmetry realized by the appropriate transformations in 1D harmonic superspace, the general mathcal{N} = 4, 1D superfield vielbein and a set of 2(n + 1) analytic “matter” superfields representing (n + 1) off-shell supermultiplets (4, 4, 0). Both superfield and component actions are given for the simplest QK models with the manifolds ℍHn = Sp(1, n)/[Sp(1) × Sp(n)] and ℍPn = Sp(1 + n)/[Sp(1) × Sp(n)] as the bosonic targets. For the general case the relevant superfield action and constraints on the (4, 4, 0) “matter” superfields are presented. Further generalizations are briefly discussed.