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arXiv · 1711.08734

${\cal N}{=}\,4$ supersymmetric mechanics on curved spaces

Nikolay Kozyrev·Sergey Krivonos·Olaf Lechtenfeld·Armen Nersessian·Anton Sutulin
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Abstract

We present ${\cal N}{=}\,4$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten-Dijkgraaf-Verlinde-Verlinde equations specified by the presence of the manifold's curvature tensor. Solutions of original Witten-Dijkgraaf-Verlinde-Verlinde equations and related prepotentials defining ${\cal N}{=}\,4$ superconformal mechanics in flat space can be lifted to $so(n)$-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of $n$ copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.

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Nikolay Kozyrev, Sergey Krivonos, Olaf Lechtenfeld, Armen Nersessian, Anton Sutulin. 2018-04-07. ${\cal N}{=}\,4$ supersymmetric mechanics on curved spaces. https://doi.org/10.1103/physrevd.97.085015

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