Details
| Original language | English |
|---|---|
| Article number | 101702 |
| Journal | Physical Review D |
| Volume | 96 |
| Issue number | 10 |
| Publication status | Published - 2017 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Physical Review D, Vol. 96, No. 10, 101702, 2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and N=4 mechanics
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. 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: © 2017 American Physical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85037130296&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.96.101702
DO - 10.1103/PhysRevD.96.101702
M3 - Article
AN - SCOPUS:85037130296
VL - 96
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 10
M1 - 101702
ER -