gravitino

In supergravity theories combining general relativity and supersymmetry, the gravitino () 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  ħ and therefore obeys the Rarita–Schwinger equation. The gravitino field is conventionally written as ψμα with a four-vector index and a spinor index. For one would get negative norm modes, as with every massless particle of spin 1 ħ or higher. These modes are unphysical, and for consistency there must be a gauge symmetry which cancels these modes: , where εα(x) is a spinor function of spacetime. This gauge symmetry is a local supersymmetry transformation, and the resulting theory is supergravity.