From linear to non-linear SUSY and back again

Abstract

Abstract:We show that couplings of the goldstino field, appearing when global supersymmetry is broken, can always be described in superspace by means of a nilpotent chiral superfield X, satisfying X 2 = 0. This applies to both F-term and D-term supersymmetry breaking, even when the supersymmetry breaking model admits a linear description.

Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms

“…Since the action (2.29) does not contain auxiliary fields, as a first step in order to prove the aforementioned equivalence we parametrize the vector V in order to separate its auxiliary degrees of freedom from the propagating ones. To this purpose, we split it into two pieces [54]…”

“…As we are going to argue, a mismatch is present between the two models, which points to the fact that not all theories with a D-term breaking will match with the Bagger-Galperin in the weak-field limit. Within the framework of non-linear supersymmetry, the Lagrangian (3.8) has been recast in the languange of constrained superfields in [54]. Its form is…”

A superfield constraint for N $$ \mathcal{N} $$ = 2 → N $$ \mathcal{N} $$ = 0 breaking

“…As we shall see, however, away from a singular corner the solution of C 3 implements the total breaking of supersymmetry. Let us also stress that the setting that we are exploring for the total breaking differs from the one captured by extensions of the N = 2 Volkov-Akulov Lagrangian (see [68][69][70] for a recent comprehensive discussion): when starting from an N = 2 vector multiplet, the low-energy dynamics that we are describing involves a vector field A µ , in addition to the expected goldstini. As we shall see, the N = 2 vector multiplet will enter the equations and the effective Lagrangian only through the abelian field strength, as in the Born-Infeld construction of [55] or in the model of [7,8] that rests on the constraints X 2 = XW α = 0, so that the final spectrum will include a massless vector field.…”

Liberated $$ \mathcal{N} $$ = 1 supergravity

“…These constraints have been studied in detail in [47,48] and the splitting (4.7) follows the logic discussed in [46]. The superfield Z is in fact the one constructed by Lindström and Roček in [18].…”

“…A method to find the equivalent theory in terms of constrained superfields has been explained in [46]. We wish to present here the supergravity theory which is equivalent to (3.19) in terms of constrained superfields.…”