Supergravity
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A supergravity theory is a field theory combining supersymmetry and general relativity.
Like any field theory of gravity a supergravity theory contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries. Supergravity theories are believed to be the only consistent theories of interacting spin 3/2 fields.
A supergravity theory is generally the zero-length limit of a superstring theory (i.e., the limit in which the string is approximated as having zero length, and treated as a dimensionless point-particle), with the exception of "maximal" 11-dimensional supergravity, which is a limit of M-theory (most likely the limit in which the membranes are treated as having zero volume).
The underlying spacetime is a supermanifold and its symmetries are superdiffeomorphisms.