Extended supersymmetry and BPS solutions in baby Skyrme models

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 a l l 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.