Geometry of N=4, d=1 nonlinear supermultiplet

Abstract

We construct the general action for $N=4,d=1$ nonlinear supermultiplet including the most general interaction terms which depend on the arbitrary function $h$ obeying the Laplace equation on $S^3$. We find the bosonic field $B$ which depends on the components of nonlinear supermultiplet and transforms as a full time derivative under N=4 supersymmetry. The most general interaction is generated just by a Fayet-Iliopoulos term built from this auxiliary component. Being transformed through a full time derivative under $N=4,d=1$ supersymmetry, this auxiliary component $B$ may be dualized into a fourth scalar field giving rise to a four dimensional $N=4,d=1$ sigma-model. We analyzed the geometry in the bosonic sector and find that it is not a hyper-Kähler one. With a particular choice of the target space metric $g$ the geometry in the bosonic sector coincides with the one which appears in heterotic $(4,0)$ sigma-model in $d=2$.

9 pages, LaTeX file, PACS: 11.30.Pb, 03.65.-w

References in corpus (3)

• N=4, d=1 tensor multiplet and hyper-Kahler sigma-models
• Hyper-Kaehler geometry and dualization
• Hyper-Kahler geometries and nonlinear supermultiplets

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• Generic N=4 supersymmetric hyper-Kähler sigma models in D=1
• N=8 supersymmetric mechanics on the sphere S^3