TY - JOUR

T1 - N=4 supersymmetric mechanics on curved spaces

AU - Kozyrev, Nikolay

AU - Krivonos, Sergey

AU - Lechtenfeld, Olaf

AU - Nersessian, Armen

AU - Sutulin, Anton

N1 - Funding Information: We are grateful to M. Feigin and A. Veselov for stimulating discussions. This work was partially supported by the Heisenberg-Landau program and has been performed within the ICTP Programs AF-04 and NT-04. The work of N. K. and S. K. was partially supported by Russian Science Foundation Grant No. 14-11-00598, the one of A. S. by RFBR Grants No. 15-02-06670 and No. 18-52-05002 Arm-a. The work of A. N. was partially supported by the Armenian State Committee of Science Grants No. 15T-1C367 and No. 18RF-002. This article is based upon work from COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology).

PY - 2018/4/15

Y1 - 2018/4/15

N2 - We present 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 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.

AB - We present 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85047131646&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1711.08734

DO - 10.48550/arXiv.1711.08734

M3 - Article

AN - SCOPUS:85047131646

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 8

M1 - 085015

ER -