Note on supersymmetric Dirac-Born-Infeld action with Fayet-Iliopoulos term

TL;DR

This paper investigates the supersymmetric Dirac-Born-Infeld action with Fayet-Iliopoulos terms, revealing that on-shell it is equivalent to a standard supersymmetric DBI action with redefined tension, up to certain effective interactions.

Contribution

It demonstrates the on-shell equivalence of a supersymmetric DBI action with FI term to a standard form with redefined tension, clarifying the role of FI terms in such models.

Findings

On-shell equivalence to standard supersymmetric DBI without FI term

Reinterpretation of FI term effects as tension redefinition

Validity up to order mass-dimension 12 interactions

Abstract

We study the Dirac-Born-Infeld (DBI) action with one linear and one non-linear supersymmetry in the presence of a constant Fayet-Iliopoulos (FI) D-term added explicitly or through a deformation of supersymmetry transformations. The linear supersymmetry appears to be spontaneously broken since the D auxiliary field gets a non-vanishing vacuum expectation value and an extra term proportional to the FI parameter involving fermions emerges in the non-linear formulation of the action written recently. However in this note, we show that on-shell this action is equivalent to a standard supersymmetric DBI action ${\it without}$ FI term but with redefined tension, at least up to order of mass-dimension 12 effective interactions.