Abstract
We consider mathcal{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 α′.
Highlights
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
Once we investigate the source of the supersymmetry breaking in the alternative form of the action, we find that it corresponds to the new Fayet-Iliopoulos D-term of [8]
As we prove in the appendix A.3, any Lagrangian of the form (2.12), which transforms under supersymmetry as (2.13), is equivalent to a Lagrangian of the type (A.19) written in terms of the standard non-linear realizations of supersymmetry, with the goldstino transforming as the Volkov-Akulov fermion (A.3)
Summary
A subclass of these actions has a second supersymmetry non-linearly realized, as was derived in [26] by Bagger and Galperin, who discussed the possible relation with D3-branes. We start from the known formulation in terms of a linear representation of supersymmetry, namely an N = 1 vector superfield, and we recast the model into an equivalent form, in which the spontaneously broken supersymmetry is manifest and described by superspace. We obtain a Born-Infeld Lagrangian in which the goldstino sector is described by a Volkov-Akulov fermion [37,38,39,40,41] and supersymmetry is manifestly nonlinearly realized [42]
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