SU(2|1) supersymmetric mechanics on curved spaces
Nikolay Kozyrev (Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia); Sergey Krivonos (Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia); Olaf Lechtenfeld (Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstrasse 2, Hannover, 30167, Germany); Anton Sutulin (Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980, Russia)
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.
