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We discuss a supersymmetric extension of a non-relativistic Chern-Simonsmatter theory, known as the SUSY Jackiw-Pi model, in a harmonic trap. We showthat the non-relativistic version of the superconformal symmetry, called thesuper-Schr\"odinger symmetry, is not spoiled by an external field including theharmonic potential. It survives as a modified symmetry whose generators haveexplicit time dependences determined by the strength of the trap, the rotationvelocity of the system and the fermion number chemical potential. We construct1/3 BPS states of trapped Jackiw-Pi vortices preserving a part of the modifiedsuperconformal symmetry and discuss fluctuations around static BPSconfigurations. In addition to the bosonic massive Nambu-Goldstone modes, wefind that there exist massive Nambu-Goldstone fermions associated with brokenmodified super-Schr\"odinger symmetry generators. Furthermore, we find thateigenmodes form supermultiplets of a modified supersymmetry preserved by thestatic BPS backgrounds. As a consequence of the modified supersymmetry,infinite towers of explicit spectra can be found for eigenmodes correspond- ingto bosonic and fermionic lowest Landau levels.

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