supergravities

Supergravity is a field theory that unifies general relativity with supersymmetry by promoting supersymmetry to a local symmetry. The gauge field for local supersymmetry is the gravitino, a spin-3/2 fermion, while the graviton remains the spin-2 mediator of gravity. The resulting theory couples gravity to matter and gauge fields in a way dictated by local supersymmetry. In four dimensions, supergravity theories are often labeled by N, the number of independent supercharges; their field content forms multiplets that include the graviton, gravitino, and additional bosonic and fermionic fields depending on N.

The first supergravity theory was constructed in 1976 by Freedman, van Nieuwenhuizen and Ferrara, with related work by Deser and Zumino. Since then, theories with extended supersymmetry (N>1) were developed, and the maximal dimension for an interacting supergravity theory is eleven, described by 11-dimensional supergravity discovered by Cremmer, Julia and Scherk. In four dimensions, notable cases include N=1, N=2, N=4 and the maximally supersymmetric N=8 theory; extended theories in higher dimensions can be compactified to yield lower-dimensional models. In many cases the supersymmetry algebra closes only on-shell, and off-shell formulations with a finite set of auxiliary fields exist only for some cases.

Supergravity is important as the low-energy limit of string theory and as a framework for studying quantum gravity and holography. It provides the starting point for compactifications that produce four-dimensional physics and serves as a setting for anti-de Sitter/CFT dualities, with certain AdS backgrounds arising as solutions to supergravity theories. It thus connects to broader developments in high-energy theory, including M-theory and the study of supersymmetric vacua and dualities.