Partial $N$ = 2 supersymmetry breaking and deformed hypermultiplets

We study partial supersymmetry breaking from $N$ = 2 to $N$ = 1 by adding non-linear terms to the $N$ = 2 supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial breaking to occur, we systematically use $N$ = 2 projective superspace with central charges to provide a streamlined setup. For deformed $O$(2) and $O$(4) hypermultiplets, besides reproducing known results, we describe new models exhibiting partial supersymmetry breaking with and without higher-derivative interactions.