# $\mathcal N=2$ Supersymmetry Deformations, Electromagnetic Duality and Dirac-Born-Infeld Actions

## TL;DR

This paper explores deformations of $
=2$ supersymmetry in vector multiplets, revealing conditions for partial supersymmetry breaking and analyzing the effects on Dirac-Born-Infeld actions, including induced FI terms and fermionic modifications.

## Contribution

It introduces a novel magnetic deformation framework for $
=2$ supersymmetry, linking it to scalar potential minima and modifications in DBI actions with non-linear supersymmetry.

## Key findings

- Deformation induces scalar potential minima with partial supersymmetry breaking.
- Magnetic deformation introduces FI D-terms via the theta-angle.
- On-shell actions differ by fermionic contributions from standard DBI+FI.

## Abstract

We study the general deformation of $\mathcal N=2$ 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 $\mathcal N=2\to \mathcal N=1$ 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 $\mathcal N=2$ 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.