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

Abstract

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincaré 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 "Lévy-Leblond-type" equations which, together, carry an N=2 superSchrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincaré algebra.

arXiv comment14 pages, no figures. Published version

References in corpus (19)

• Galilean Conformal Algebras and AdS/CFT
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Schr"odinger invariance and space-time symmetries
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Deformed Heisenberg algebra with reflection
• On Schrödinger superalgebras
• Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems
• On AdS/CFT of Galilean Conformal Field Theories
• Non-relativistic conformal symmetries in fluid mechanics
• Spinors in non-relativistic Chern-Simons electrodynamics
• Bosons, fermions and anyons in the plane, and supersymmetry
• The exotic conformal Galilei algebra and nonlinear partial differential equations
• On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
• R-deformed Heisenberg algebra, anyons and d=2+1 supersymmetry
• Interaction via reduction and nonlinear superconformal symmetry
• Spinor vortices in non-relativistic Chern-Simons theory
• Dynamal (super)symmetries of monopoles and vortices
• Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons

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• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Supersymmetric content of the Dirac and Duffin-Kemmer-Petiau equations
• (p,q) D=3 Poincare supergravities from Lie algebra expansions
• Splitting the Dirac equation: the case of longitudinal potentials
• Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism
• Superfield approach to higher derivative N=1 superconformal mechanics
• On nonrelativistic 3D Spin-1 theories
• Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra