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arXiv · 1710.00884

Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and ${\cal N}{=}\,4$ mechanics

Nikolay Kozyrev·Sergey Krivonos·Olaf Lechtenfeld·Armen Nersessian·Anton Sutulin
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Abstract

We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from ${\mathbb R}^n$ to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with ${\cal N}{=}\,4$ 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.

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Nikolay Kozyrev, Sergey Krivonos, Olaf Lechtenfeld, Armen Nersessian, Anton Sutulin. 2017-10-02. Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and ${\cal N}{=}\,4$ mechanics. https://doi.org/10.1103/physrevd.96.101702

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