4D N = 1 supergravity

In supersymmetry, 4D ${\displaystyle {\mathcal {N}}=1}$ supergravity is the theory of supergravity in four dimensions with a single supercharge. It contains exactly one supergravity multiplet, consisting of a graviton and a gravitino, but can also have an arbitrary number of chiral and vector supermultiplets, with supersymmetry imposing stringent constraints on how these can interact. The theory is primarily determined by three functions, those being the Kähler potential, the superpotential, and the gauge kinetic matrix. Many of its properties are strongly linked to the geometry associated to the scalar fields in the chiral multiplets. After the simplest form of this supergravity was first discovered, a theory involving only the supergravity multiplet, the following years saw an effort to incorporate different matter multiplets, with the general action being derived in 1982 by Eugène Cremmer, Sergio Ferrara, Luciano Girardello, and Antonie Van Proeyen.^[1][2]

This theory plays an important role in many Beyond the Standard Model scenarios. Notably, many four-dimensional models derived from string theory are of this type, with supersymmetry providing crucial control over the compactification procedure. The absence of low-energy supersymmetry in our universe requires that supersymmetry is broken at some scale. Supergravity provides new mechanisms for supersymmetry breaking that are absent in global supersymmetry, such as gravity mediation. Another useful feature is the presence of no-scale models, which have numerous applications in cosmology.