Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms

We consider ${\cal N}=1$ supersymmetric Born-Infeld actions that have a second non-linear supersymmetry. We focus on the model proposed by Bagger and Galperin and show that the breaking of the second supersymmetry is sourced by the new Fayet-Iliopoulos D-term. Interpreting such an action as the effective theory of a space-filling (anti) D3-brane leads to an expression for the new Fayet-Iliopoulos parameter in terms of the brane tension and $\alpha'$.