Geometry of N=4, d=1 nonlinear supermultiplet

TL;DR

This paper constructs the most general action for N=4, d=1 nonlinear supermultiplet, exploring its geometric properties and showing it leads to a non-hyper-Kähler sigma-model with connections to heterotic models.

Contribution

It introduces the general form of the N=4, d=1 nonlinear supermultiplet action, including the role of an auxiliary component and its dualization, and analyzes the resulting geometry.

Findings

The auxiliary component B transforms as a total derivative under supersymmetry.

The general interaction is generated by a Fayet-Iliopoulos term.

The bosonic sector's geometry is not hyper-Kähler, matching heterotic (4,0) sigma-model geometry.

Abstract

We construct the general action for $N=4, d=1$ nonlinear supermultiplet including the most general interaction terms which depend on the arbitrary function $h$ obeying the Laplace equation on $S^3$. We find the bosonic field $B$ which depends on the components of nonlinear supermultiplet and transforms as a full time derivative under N=4 supersymmetry. The most general interaction is generated just by a Fayet-Iliopoulos term built from this auxiliary component. Being transformed through a full time derivative under $N=4, d=1$ supersymmetry, this auxiliary component $B$ may be dualized into a fourth scalar field giving rise to a four dimensional $N=4, d=1$ sigma-model. We analyzed the geometry in the bosonic sector and find that it is not a hyper-K\"ahler one. With a particular choice of the target space metric $g$ the geometry in the bosonic sector coincides with the one which appears in heterotic $(4,0)$ sigma-model in $d=2$.