Abstract
We construct supergravity models where the goldstino multiplet has a gravitational origin, being dual to the chiral curvature superfield. Supersymmetry is nonlinearly realized due to a nilpotent constraint, while the goldstino arises from γ–traces of the gauge–invariant gravitino field strength. After duality transformations one recovers, as expected, the standard Volkov–Akulov Lagrangian coupled to Supergravity, but the gravitational origin of the goldstino multiplet restricts the available types of matter couplings. We also construct explicitly some inflationary models of this type, which contain both the inflaton and the nilpotent superfield.
Highlights
We construct supergravity models where the goldstino multiplet has a gravitational origin, being dual to the chiral curvature superfield
After duality transformations one recovers, as expected, the standard Volkov-Akulov Lagrangian coupled to Supergravity, but the gravitational origin of the goldstino multiplet restricts the available types of matter couplings
In [36], the chiral curvature multiplet R was subject to the constraint R2 = 0, which translated into the corresponding constraint X2 = 0 for the goldstino multiplet, one of the two chiral multiplets present in the two-derivative dual Supergravity
Summary
Where the subscripts identify D and F superspace densities and S0 is the chiral compensator field. One can illustrate the amusing properties of this system rather clearly in a Minkowski vacuum, while confining the attention to terms that are at most quadratic in the gravitino In this case the relevant parts of local Supersymmetry variations in [11, 12], which do not involve the auxiliary field Aμ, read δ ψμ L = ∂μ ǫL u 6 γμ ǫR , δ u = i ǫR γμν ∂μ ψν R iu 2. The analogies go even further, since similar constructs enter the higher-spin equations of [78,79,80,81,82], where higher-derivative compensators built from the original Fronsdal field [83, 84] result in geometric expressions involving higher-spin curvatures
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