A field theory combining supersymmetry and general relativity, extending Einstein's equations.Supergravity is a theoretical framework that combines supersymmetry with general relativity. In supersymmetry, every particle has a superpartner with a spin differing by half a unit; when this symmetry is made local, it necessitates the introduction of a graviton's superpartner, the gravitino, and the resulting theory is supergravity. It extends Einstein's equations by incorporating fermionic fields and higher-order corrections, providing a more complete description of spacetime at quantum scales.
Supergravity was first constructed in 1976 by Daniel Z. Freedman, Sergio Ferrara, and Peter van Nieuwenhuizen, and independently by Stanley Deser and Bruno Zumino.
In supergravity, the gravitational field is described by a metric tensor, but also by a spin-3/2 field (the gravitino). The theory is built by requiring that the action is invariant under local supersymmetry transformations. This leads to a set of field equations that reduce to Einstein's equations in the classical limit, but include additional terms involving fermions and possibly higher-order curvature corrections. Supergravity is a key ingredient in string theory, where it emerges as the low-energy effective field theory.
It is primarily used in theoretical physics, particularly in string theory and in models of early universe cosmology, where it helps address the singularity problem and provides a framework for understanding the unification of forces.
The maximal supergravity in four dimensions, N=8 supergravity, has been shown to have remarkable ultraviolet finiteness properties, suggesting it might be a finite quantum theory of gravity even without string theory.











