The Fayet-Iliopoulos term and nonlinear self-duality

TL;DR

This paper explores how adding a Fayet-Iliopoulos term to the N=1 supersymmetric Born-Infeld action affects supersymmetry breaking and self-duality, revealing new deformations and their implications for nonlinear supersymmetric electrodynamics.

Contribution

It introduces a novel deformation of the N=1 supersymmetric Born-Infeld action incorporating the Fayet-Iliopoulos term, with analysis of its effects on supersymmetry breaking and duality properties.

Findings

Fayet-Iliopoulos term allows partial N=2 to N=1 supersymmetry breaking.

A two-parameter duality-covariant deformation of the Born-Infeld action is proposed.

The role of the Volkov-Akulov action in self-dual nonlinear supersymmetric models is clarified.

Abstract

The N = 1 supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken N = 2 rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the Fayet-Iliopoulos term without losing the second nonlinearly realized supersymmetry. Although the first supersymmetry then becomes spontaneously broken, the deformed action still describes partial N = 2 to N = 1 supersymmetry breaking. The unbroken supercharges in this theory correspond to a different choice of N = 1 subspace in the N = 2 superspace, as compared with the undeformed case. Implications of the Fayet-Iliopoulos term for general models for self-dual nonlinear supersymmetric electrodynamics are discussed. The known ubiquitous appearance of the Volkov-Akulov action in such models is explained. We also present a two-parameter duality-covariant deformation of the N = 1 supersymmetric Born-Infeld action as a model for partial breaking of N = 2 supersymmetry.