supergravity

Supergravity is a field theory that unifies general relativity with supersymmetry by promoting supersymmetry to a local gauge symmetry. The fundamental fields include the graviton, a massless spin-2 particle, and its fermionic superpartner, the gravitino, which has spin 3/2. Local supersymmetry relates bosonic and fermionic degrees of freedom and requires a supersymmetric partner for gravity. The action typically combines the Einstein-Hilbert term with a Rarita-Schwinger term for the gravitino, and may include auxiliary fields in off-shell formulations.

Historically, the first four-dimensional supergravity theories were constructed in 1976 by Freedman, van Nieuwenhuizen and Ferrara. The theory was extended to include additional supersymmetry generators (N>1) and, in eleven dimensions, became the unique maximal supergravity theory discovered by Cremmer, Julia and Scherk. Dimensional reduction of eleven-dimensional supergravity yields a family of lower-dimensional supergravities with rich scalar, gauge, and duality structures. In string theory, supergravity appears as the low-energy effective field theory of various superstring theories and of M-theory, and maximally supersymmetric eleven-dimensional supergravity is viewed as a corner of that framework.

Applications and role: supergravity provides a framework for studying quantum gravity aspects, AdS/CFT, flux compactifications, and model building in high-energy physics. It offers insights into how gravity might be incorporated into a quantum-consistent theory of matter. Limitations: like general relativity, supergravity by itself is non-renormalizable in four dimensions; it is considered an effective field theory valid up to a cutoff, with full UV completion given by string/M-theory. Experimental signs of supersymmetry have not yet been observed.