Gravitino

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In supergravity theories combining general relativity and supersymmetry, the gravitino (
G͂
) is the gauge fermion supersymmetric partner of the hypothesized graviton. It has been suggested as a candidate for dark matter.

If it exists, it is a fermion of spin ⁠3/2⁠ and therefore obeys the Rarita–Schwinger equation. The gravitino field is conventionally written as ψ_μα with μ = 0, 1, 2, 3 a four-vector index and α = 1, 2 a spinor index. For μ = 0 one would get negative norm modes, as with every massless particle of spin 1 or higher. These modes are unphysical, and for consistency there must be a gauge symmetry which cancels these modes: δψ_μα = ∂_με_α, where ε_α(x) is a spinor function of spacetime. This gauge symmetry is a local supersymmetry transformation, and the resulting theory is supergravity.

Thus the gravitino is the fermion mediating supergravity interactions, just as the photon is mediating electromagnetism, and the graviton is presumably mediating gravitation. Whenever supersymmetry is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken. This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem of the Standard Model, the gravitino cannot be more massive than about 1 TeV/c².