Planar Super-Landau Models

TL;DR

This paper extends super-Landau models to the planar limit, revealing ghost-free levels and supermultiplet structures linked to fermionic gauge invariance, advancing understanding of supersymmetric quantum systems.

Contribution

It provides the first solution of super-Landau models in the planar limit, analyzing ghost-free levels and supermultiplet formations related to fermionic gauge invariance.

Findings

Only the lowest level is ghost-free for M=0.

No ghosts in the first [2M]+1 levels for M>0.

Levels form short supermultiplets when 2M is an integer.

Abstract

In previous papers we solved the Landau problems, indexed by 2M, for a particle on the ``superflag'' S U (2|1)/[U (1) x U (1)], the M = 0 case being equivalent to the Landau problem for a particle on the ``supersphere'' S U (2|1)/[U (1|1)]. Here we solve these models in the planar limit. For M = 0 we have a particle on the complex superplane C(1|1) ; its Hilbert space is the tensor product of that of the Landau model with the 4-state space of a ``fermionic'' Landau model. Only the lowest level is ghost-free, but for M > 0 there are no ghosts in the first [2M ]+1 levels. When 2M is an integer, the ([2M ] + 1)th level states form short supermultiplets as a consequence of a fermionic gauge invariance analogous to the ``kappa-symmetry'' of the superparticle.