N=4 Supersymmetric Landau Models

TL;DR

This paper introduces the first super Landau model with N=4 worldline supersymmetry and target space supersymmetry ISU(2|2), revealing hidden symmetries and detailed structure of wave functions on R^4.

Contribution

It constructs a novel super Landau model with both manifest and hidden N=4 supersymmetry, extending previous models and analyzing its symmetry and wave function structure.

Findings

Wave functions form atypical multiplets of SU(2|2)

Hidden second N=4 supersymmetry closes on worldline SU(2|2)

Background gauge field is self-dual on R^4

Abstract

We present the first example of super Landau model with both N=4 worldline supersymmetry and non-trivial target space supersymmetry ISU(2|2). The model also reveals a hidden second N=4 supersymmetry which, together with the manifest one, close on a worldline SU(2|2). We start from an off-shell action in bi-harmonic N=4, d=1 superspace and come to the component action with four bosonic and four fermionic fields. Its bosonic core is the action of generalized U(1) Landau model on R^4 considered some time ago by Elvang and Polchinski. At each Landau level N>0 the wave functions are shown to form "atypical" (2N + 2N)-dimensional multiplets of the worldline supergroup SU(2|2). Some states have negative norms, but this trouble can be evaded by redefining the inner product, like in other super Landau models. We promote the action to the most general form compatible with off-shell N=4 worldline supersymmetry and find the corresponding background U(1) gauge field to be generic self-dual on R^4 and the target superspace metric to remain flat.