N=4 Superconformal Mechanics and the Potential Structure of AdS Spaces

TL;DR

This paper explores the dynamics of an N=4 superconformal spinning particle in curved backgrounds, revealing that such backgrounds must be Kähler-like manifolds, with AdS spaces fitting into this class, using superfield formalism.

Contribution

It demonstrates that N=4 superconformal symmetry constrains the background to be a Kähler-like manifold generated by a superpotential, including AdS spaces.

Findings

AdS spaces are Kähler-like manifolds with superpotential.

N=4 superconformal symmetry requires specific geometric structures.

The superfield formalism effectively describes the particle dynamics.

Abstract

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The $SU(2)_{local}\times SU(2)_{global}$ N=4 superconformal symmetry of the particle action requires the background to be a real "K\"ahler-like" manifold whose metric is generated by a sigma-model superpotential. The anti-de-Sitter spaces are shown to belong to this class of manifolds.