Goldstino superfields for spontaneously broken $ \mathcal{N} = 2 $ supersymmetry

We examine spontaneously broken $ \mathcal{N} = 2 $ supersymmetry in four dimensions and associate a spinor superfield with each Goldstino via a finite supersymmetry transformation with parameters that are the Grassmann coordinates of $ \mathcal{N} = 2 $ superspace. Making use of a special choice of coset parametrization allows us to develop a version of nonlinearly realized $ \mathcal{N} = 2 $ supersymmetry for which the associated Goldstino superfields are defined on harmonic superspace, thereby providing a natural mechanism for construction of a Goldstino action. The corresponding superfield Lagrangian is an O(4) multiplet. This property is used to reformulate the Goldstino action in projective superspace and in conventional $ \mathcal{N} = 2 $ superspace. We show how to generate matter couplings of the Goldstinos to supersymmetric matter using the $ \mathcal{N} = 2 $ harmonic, projective and full superspaces. As a bi-product of our consideration, we also derive an $ \mathcal{N} = 2 $ chiral Goldstino action.