Abstract
We study the Dirac-Born-Infeld (DBI) action with one linear and one nonlinear 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 without FI term but with redefined tension, at least up to order of mass-dimension 12 effective interactions.
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