Partial ${\cal N}=2$ Supersymmetry Breaking and Deformed Hypermultiplets

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