• Open Access

N=4 supersymmetric mechanics on curved spaces

Nikolay Kozyrev, Sergey Krivonos, Olaf Lechtenfeld, Armen Nersessian, and Anton Sutulin
Phys. Rev. D 97, 085015 – Published 16 April 2018

Abstract

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.

  • Received 22 December 2017

DOI:https://doi.org/10.1103/PhysRevD.97.085015

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Nikolay Kozyrev1,*, Sergey Krivonos1,†, Olaf Lechtenfeld2,‡, Armen Nersessian1,3,§, and Anton Sutulin1,∥

  • 1Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
  • 2Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
  • 3Yerevan Physics Institute, 2 Alikhanian Brothers Street, 0036 Yerevan, Armenia

  • *nkozyrev@theor.jinr.ru
  • krivonos@theor.jinr.ru
  • lechtenf@itp.uni-hannover.de
  • §arnerses@ysu.am
  • sutulin@theor.jinr.ru

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Issue

Vol. 97, Iss. 8 — 15 April 2018

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