Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit

TL;DR

This paper unifies planar Dirac and topologically massive vector gauge fields into a supermultiplet, revealing supersymmetry structures and deriving non-relativistic limits with superSchr"odinger symmetry, advancing understanding of supersymmetric field theories.

Contribution

It introduces a supermultiplet unifying Dirac and gauge fields without auxiliary fields, and explores the emergence of superPoincaré and superSchr"odinger symmetries in non-relativistic limits.

Findings

Supermultiplet unifies Dirac and gauge fields.

Emergence of superPoincaré symmetry from osp(1|2).

Non-relativistic limit yields superSchr"odinger symmetry.

Abstract

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincar\'e symmetry emerges from the $osp(1|2)$ supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "L\'evy-Leblond-type" equations which, together, carry an N=2 superSchr\"odinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincar\'e algebra.