We construct the N=2 supersymmetric extensions of different models containing a Chern-Simons term and study their BPS structure. We find that the coupling of the Chern-Simons term to the general gauged nonlinear σ-model allows for general potentials depending on the K\"{a}hler metric and preserving two supersymmetries. We construct from supersymmetry the potentials that allow for BPS structures in different CPN models coupled to Chern-Simons and Maxwell terms. We also couple the Chern-Simons term to a higher-derivative field theory (the baby Skyrme model) and study its SUSY extension and BPS structure.
@article{arxiv.1807.09612,
title = {SUSY Chern-Simons $\mathbb{CP}^N$ and baby Skyrme models and their BPS structures},
author = {Jose M. Queiruga},
journal= {arXiv preprint arXiv:1807.09612},
year = {2019}
}