${\cal N}{=}\,4$ supersymmetric mechanics on curved spaces
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.08734
- arXiv:
- arXiv:1711.08734
- Bibcode:
- 2017arXiv171108734K
- Keywords:
-
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 1+10 pages, v2: minor changes, v3: reference added, published version