New variant of N=4 superconformal mechanics

TL;DR

This paper develops a new N=4 superconformal mechanics model based on the supergroup D(2,1;alpha), featuring a unique combination of fields, invariant actions, and a target space geometry that is a cone over S^2, with potential links to AdS_2 x S^2 superparticle dynamics.

Contribution

It introduces a novel N=4 superconformal mechanics model with invariant actions, extended supersymmetry, and a cone-shaped target space, expanding the understanding of superconformal systems.

Findings

Constructed invariant off-shell N=4 and N=2 superfield actions.

Identified a superconformal invariant extending the dilaton potential.

Target space geometry is a cone over S^2 for non-zero alpha.

Abstract

Proceeding from a nonlinear realization of the most general N=4, d=1 superconformal symmetry, associated with the supergroup D(2,1;alpha), we construct a new model of nonrelativistic N=4 superconformal mechanics. In the bosonic sector it combines the worldline dilaton with the fields parametrizing the R-symmetry coset S^2 ~ SU(2)/U(1). We present invariant off-shell N=4 and N=2 superfield actions for this system and show the existence of an independent N=4 superconformal invariant which extends the dilaton potential. The extended supersymmetry requires this potential to be accompanied by a d=1 WZW term on S^2. We study the classical dynamics of the bosonic action and the geometry of its sigma-model part. It turns out that the relevant target space is a cone over S^2 for any non-zero alpha \neq \pm 1/2. The constructed model is expected to be related to the `relativistic' N=4 mechanics of the AdS_2 times S^2 superparticle via a nonlinear transformation of the fields and the time variable.