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Generic N=4 supersymmetric hyper-Kähler sigma models in D=1

S. Bellucci·S. Krivonos·A. Shcherbakov
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Abstract

We analyse the geometry of four-dimensional bosonic manifolds arising within the context of $N=4, D=1$ supersymmetry. We demonstrate that both cases of general hyper-Kähler manifolds, i.e. those with translation or rotational isometries, may be supersymmetrized in the same way. We start from a generic N=4 supersymmetric three-dimensional action and perform dualization of the coupling constant, initially present in the action. As a result, we end up with explicit component actions for $N=4, D=1$ nonlinear sigma-models with hyper-Kähler geometry (with both types of isometries) in the target space. In the case of hyper-Kähler geometry with translational isometry we find that the action possesses an additional hidden N=4 supersymmetry, and therefore it is N=8 supersymmetric one.

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S. Bellucci, S. Krivonos, A. Shcherbakov. 2006-11-24. Generic N=4 supersymmetric hyper-Kähler sigma models in D=1. https://doi.org/10.1016/j.physletb.2006.12.014

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