SU(2$|$1) supersymmetric mechanics on curved spaces

Abstract

We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV equations specified by the manifold's metric and curvature tensor. We consider the most general $u(2)$-valued prepotential, which contains both types (with and without spin variables), previously considered only separately. For the case of real Kähler manifolds we construct all possible interactions. For isotropic ($so(n)$-invariant) spaces we provide admissible prepotentials for any solution to the curved WDVV equations. All known one-dimensional SU$(2|1)$ supersymmetric models are reproduced.

1+6 pages

References in corpus (7)

• Supersymmetric Calogero models by gauging
• N=4 superconformal Calogero models
• N=4 mechanics, WDVV equations and roots
• Supersymmetric Kähler oscillator in a constant magnetic field
• Deformed supersymmetric quantum mechanics with spin variables
• $\mathcal{N}=4$ supersymmetric mechanics on curved spaces
• Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and $\mathcal{N}=4$ mechanics

Cited by in corpus (7)

• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• WDVV equations and invariant bi-Hamiltonian formalism
• The curved WDVV equations and superfields
• Conformal bridge in a cosmic string background
• A three-dimensional superconformal quantum mechanics with $sl(2|1)$ dynamical symmetry
• SU$(2|1)$ supersymmetric spinning models of chiral superfields
• Superintegrable deformations of oscillator and Coulomb systems