Abstract
We present supersymmetric mechanics on -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 superconformal mechanics in flat space can be lifted to -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 copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.
- Received 22 December 2017
DOI:https://doi.org/10.1103/PhysRevD.97.085015
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Published by the American Physical Society