$$ \mathcal{N} $$ = 2 supersymmetry deformations, electromagnetic duality and Dirac-Born-Infeld actions

Abstract

Abstract We study the general deformation of $$ \mathcal{N} $$ N = 2 supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the SU(2) R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of $$ \mathcal{N} $$ N = 2 → $$ \mathcal{N} $$ N = 1 supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed $$ \mathcal{N} $$ N = 2 chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions.