Unitary Spherical Super-Landau Models

TL;DR

This paper develops a positive-definite Hilbert space metric for SU(2|1)-invariant superflag Landau models, determines their spectra, and reveals enhanced symmetries, advancing understanding of supersymmetric quantum Hall systems.

Contribution

It introduces a new Hilbert space metric ensuring unitarity and uncovers symmetry enhancement from SU(2|1) to SU(2|2) in superflag Landau models.

Findings

Hilbert space metric ensures positive definiteness

Spectrum of unitary super-Landau models determined

Symmetry enhancement from SU(2|1) to SU(2|2)

Abstract

A Hilbert space metric is found for the SU(2|1)-invariant `superflag' Landau models, parametrized by integer 2N' and real number M, such that the Hilbert space norm is positive definite. The spectrum of these unitary super-Landau models is determined. The M=0 case yields a unitary Landau model on the supersphere SU(2|1)/U(1|1) with U(1) charge 2N=2N'+1. For the generic unitary superflag model, the manifest SU(2|1) symmetry is dynamically enhanced to SU(2|2); this is the `spherical' analog of the hidden worldline supersymmetry found previously in the planar limit.