@article{f995ddbc84814c77932c3e14f67ebc53,
title = "Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and N=4 mechanics",
abstract = "We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from Rn to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with N=4 supersymmetric n-dimensional mechanics from flat to curved space. The resulting {"}curved WDVV equation{"} is written in terms of a third-rank Codazzi tensor. For every flat-space WDVV solution subject to a simple constraint, we provide a curved-space solution on any isotropic space, in terms of the rotationally invariant conformal factor of the metric.",
author = "Nikolay Kozyrev and Sergey Krivonos and Olaf Lechtenfeld and Armen Nersessian and Anton Sutulin",
note = "Funding Information: We are grateful to M. Feigin and A. Veselov for stimulating discussions. A. S. also thanks S. Kuzenko, A. Sagnotti, and D. Sorokin for valuable comments and discussions during the Ginzburg conference in Moscow. This work was partially supported by the Heisenberg-Landau program. The work of N. K. and S. K. was partially supported by RSCF Grant No. 14-11-00598, and that of A. S. was partially supported by RFBR Grant No. 15-02-06670. The work of A. N. was partially supported by the Armenian State Committee of Science Grant No. 15T-1C367. This article is based upon work from COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology). Publisher Copyright: {\textcopyright} 2017 American Physical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2017",
doi = "10.1103/PhysRevD.96.101702",
language = "English",
volume = "96",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Physical Society",
number = "10",
}