On 4D, $$ \mathcal{N} $$ = 2 deformed vector multiplets and partial supersymmetry breaking in off-shell supergravity

A bstract Electric and magnetic Fayet-Ilioupulous (FI) terms are used to engineer partial breaking of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 global supersymmetry for systems of vector multiplets. The magnetic FI term induces a deformation of the off-shell field transformations associated with an imaginary constant shift of the triplet of auxiliary fields of the vector multiplet. In this paper, we elaborate on the deformation of off-shell vector multiplets in supergravity, both in components and superspace. In a superconformal framework, the deformations are associated with (composite) linear multiplets. We engineer an off-shell model that exhibits partial local supersymmetry breaking with a zero cosmological constant. This is based on the hyper-dilaton Weyl multiplet introduced in arXiv:2203.12203, coupled to the SU(1,1)/U(1) special-Kähler sigma model in a symplectic frame admitting a holomorphic prepotential, with one compensating and one physical vector multiplet, the latter magnetically deformed.