Vortex solutions and a novel role for R-parity in an N=2N=2-supersymmetric extension of Jackiw–Pi’s chiral gauge theory

In a previous work, we have been able to settle Jackiw–Pi’s chiral gauge theory (CGT), originally proposed to describe Dirac fermions in graphene, in an N=1N=1 supersymmetric framework using a τ3τ3-QED prescription, defined by means of a single pair of gauge charged superfields, but without preserving a global phase symmetry associated, in the CGT, to the electric charge. In the present work, we propose another N=1N=1-generalisation which indeed preserves this symmetry, namely, a straightforward extension built upon a set of two pairs of (chiral) gauge-charged superfields plus an extra pair of electrically neutral superfields. We then further proceed to establish, via a dimensional reduction procedure, an N=2N=2 extension, allowing for the identification of non-perturbative features, as we put forward Bogomol’nyi equations and obtain vortex-like solutions saturating a topologically non-trivial bound. Remarkably, the bosonic projection of the N=2N=2 functional space onto the saturated regime analysed herewith reveals to be free from extra scalar degrees of freedom that would otherwise demand a phenomenological interpretation. The investigation of Jackiw–Pi’s model within an N=2N=2 complex superspace is also motivated by the assumption that an R-parity-like symmetry could provide a route to incorporate the global phase-fermion number invariance as an external-like symmetry of the theory, thus associating electric charge in the CGT to the complex covariance (super-)space for the N=2N=2-D=3 setup. We prove such a hypothesis to be realisable, as we build up the model endowed with all the symmetries required to further extend Jackiw–Pi’s chiral gauge theory.