SUSY Chern-Simons ${\mathbb{CP}}^N$ and baby Skyrme models and their BPS structures

Abstract

We construct the $\mathcal{N}=2$ 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 $\sigma$-model allows for general potentials depending on the Kähler metric and preserving two supersymmetries. We construct from supersymmetry the potentials that allow for BPS structures in different $\mathbb{C}{P}^N$ 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.

30 pages