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In a previous work, we have been able to settle Jackiw's et al. chiral gaugetheory for Dirac fermions in graphene in an N=1 supersymmetric framework, usinga tau3-QED prescription, defined by means of a single pair of gauge chargedsuperfields, but without preserving a global phase symmetry associated to theelectric charge. In the present work, we propose another N=1-generalisationwhich indeed preserves this symmetry, namely, a straightforward extension builtupon a set of two pairs of (chiral) gauge-charged superfields plus an extrapair of electrically neutral superfields. We then further proceed to establish,via a dimensional reduction procedure, an N=2 extension, allowing for theidentification of non-perturbative features, as we put forward Bogomol'nyiequations and obtain vortex-like solutions saturating a topologicallynon-trivial bound. Remarkably, the bosonic projection of the N=2 functionalspace onto the saturated regime analysed herewith reveals to be free from extrascalar degrees of freedom that would otherwise demand a phenomenologicalinterpretation. The investigation of Jackiw's model within an N=2 complexsuperspace is also motivated by the assumption that an R-parity-like symmetrycould provide a route to incorporate the global phase-fermion number invarianceas an external-like symmetry of the theory, thus associating the electriccharge in graphene to the complex covariance (super-)space for the N=2-D=3setup. We prove such a hypothesis to be realisable, as we build up the modelendowed with all the symmetries required to further extend Jackiw's chiralgauge theory.

Vortex Solutions and a Novel Role for R-parity in an N=2-Supersymmetric Model for Graphene