Extended Supersymmetry and BPS solutions in baby Skyrme models

TL;DR

This paper explores supersymmetric extensions of baby Skyrme models in 2+1 dimensions, demonstrating N=1 and N=2 SUSY formulations, and analyzing BPS solutions and equations in these models.

Contribution

It constructs N=1 and N=2 supersymmetric extensions of baby Skyrme models, including gauged versions, and derives general BPS equations for N=2 SUSY theories.

Findings

N=1 SUSY extension of CP(1) and O(3) baby Skyrme models

N=2 SUSY extensions support BPS solitons as half-BPS states

Derived general BPS equations for N=2 supersymmetric field theories

Abstract

We continue the investigation of supersymmetric extensions of baby Skyrme models in d=2+1 dimensions. In a first step, we show that the CP(1) form of the baby Skyrme model allows for the same N=1 SUSY extension as its O(3) formulation. Then we construct the N=1 SUSY extension of the gauged baby Skyrme model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a next step, we investigate the issue of N=2 SUSY extensions of baby Skyrme models. We find that all gauged and ungauged submodels of the baby Skyrme model which support BPS soliton solutions allow for an N=2 extension such that the BPS solutions are one-half BPS states (i.e., annihilated by one-half of the SUSY charges). In the course of our investigation, we also derive the general BPS equations for completely general N=2 supersymmetric field theories of (both gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear sigma model as a further, concrete example.