Massive Nambu-Goldstone Fermions and Bosons for Non-relativistic Superconformal Symmetry: Jackiw-Pi Vortices in a Trap

TL;DR

This paper explores a supersymmetric non-relativistic Chern-Simons theory with harmonic trapping, revealing massive Nambu-Goldstone modes, modified superconformal symmetry, and supermultiplet structures in vortex configurations.

Contribution

It demonstrates the preservation of super-Schrödinger symmetry in a trapped setting and constructs BPS vortex states with associated massive Nambu-Goldstone modes and supermultiplet spectra.

Findings

Existence of massive Nambu-Goldstone fermions due to broken symmetry

Construction of 1/3 BPS vortex states in a harmonic trap

Infinite eigenmode towers forming supermultiplets

Abstract

We discuss a supersymmetric extension of a non-relativistic Chern-Simons matter theory, known as the SUSY Jackiw-Pi model, in a harmonic trap. We show that the non-relativistic version of the superconformal symmetry, called the super-Schr\"odinger symmetry, is not spoiled by an external field including the harmonic potential. It survives as a modified symmetry whose generators have explicit time dependences determined by the strength of the trap, the rotation velocity of the system and the fermion number chemical potential. We construct 1/3 BPS states of trapped Jackiw-Pi vortices preserving a part of the modified superconformal symmetry and discuss fluctuations around static BPS configurations. In addition to the bosonic massive Nambu-Goldstone modes, we find that there exist massive Nambu-Goldstone fermions associated with broken modified super-Schr\"odinger symmetry generators. Furthermore, we find that eigenmodes form supermultiplets of a modified supersymmetry preserved by the static BPS backgrounds. As a consequence of the modified supersymmetry, infinite towers of explicit spectra can be found for eigenmodes correspond- ing to bosonic and fermionic lowest Landau levels.