Planar Super-Landau Models Revisited

TL;DR

This paper revisits planar super-Landau models using PT-symmetric quantum theory, revealing a family of models with spontaneous supersymmetry breaking and norm-dependent spectra, contrasting with traditional supersymmetric quantum mechanics.

Contribution

It introduces a one-parameter family of ISU(1|1)-invariant super-Landau models with positive norm and explores their spontaneous supersymmetry breaking and spectral properties.

Findings

Discovered a family of models with spontaneously broken worldline supersymmetry.

Found that state norms, not energies, depend on parameters.

Spectral discontinuity occurs when supersymmetry is restored.

Abstract

We use the methods of PT-symmetric quantum theory to find a one-parameter family of ISU(1|1)-invariant planar super-Landau models with positive norm, uncovering an `accidental', and generically spontaneously-broken, worldline supersymmetry, with charges that have a Sugawara-type representation in terms of the ISU(1|1) charges. In contrast to standard models of supersymmetric quantum mechanics, it is the norms of states rather than their energies that are parameter-dependent, and the spectrum changes discontinuously in the limit that worldline supersymmetry is restored.