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

Abstract

We present $\mathcal{N}=4$ 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 $\mathcal{N}=4$ 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.

1+10 pages, v2: minor changes, v3: reference added, published version

References in corpus (5)

• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• N=4 mechanics, WDVV equations and roots
• On the geometry of V-systems
• Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and $\mathcal{N}=4$ mechanics

Cited by in corpus (10)

• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Special Geometry, Hessian Structures and Applications
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• SU(2$|$1) supersymmetric mechanics on curved spaces
• Probing the holomorphic anomaly of the $D=2,\mathcal{N}=2$, Wess-Zumino model on the lattice
• The curved WDVV equations and superfields
• Superfield approach to higher derivative N=1 superconformal mechanics
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
• Superintegrable deformations of oscillator and Coulomb systems