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

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 $\mathcal{N}=4$ 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.

1+4 pages; v2: title change, published version

References in corpus (2)

• N=4 superconformal Calogero models
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots

Cited by in corpus (2)

• Superfield approach to higher derivative N=1 superconformal mechanics
• Hidden symmetries and nonlinear (super)algebras