Pure 4D N = 1 supergravity

In supersymmetry, pure 4D ${\displaystyle {\mathcal {N}}=1}$ supergravity describes the simplest four-dimensional supergravity, with a single supercharge and a supermultiplet containing a graviton and gravitino. The action consists of the Einstein–Hilbert action and the Rarita–Schwinger action. The theory was first formulated by Daniel Z. Freedman, Peter van Nieuwenhuizen, and Sergio Ferrara, and independently by Stanley Deser and Bruno Zumino in 1976.^[1][2] The only consistent extension to spacetimes with a cosmological constant is to anti-de Sitter space, first formulated by Paul Townsend in 1977.^[3] When additional matter supermultiplets are included in this theory, the result is known as matter-coupled 4D ${\displaystyle {\mathcal {N}}=1}$ supergravity.