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

TL;DR

This paper develops $ ext{N}=2$ supersymmetric extensions of models with Chern-Simons terms, exploring their BPS structures and potentials, including applications to $ ext{CP}^N$ and baby Skyrme models, revealing new supersymmetric BPS configurations.

Contribution

It introduces novel $ ext{N}=2$ supersymmetric models with Chern-Simons terms, analyzing their BPS structures and potential functions, especially in $ ext{CP}^N$ and baby Skyrme models.

Findings

Constructed $ ext{N}=2$ SUSY extensions with Chern-Simons and Maxwell terms.

Identified potentials compatible with BPS structures in $ ext{CP}^N$ models.

Extended Chern-Simons coupling to baby Skyrme model and studied its SUSY and BPS properties.

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 K\"{a}hler 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.