If gravity is included in the theory, so that there is local supersymmetry, then the resulting theory is called a supergravity theory and the restriction on the geometry of the moduli space becomes stronger. The moduli space must not only be Kähler, but also the Kähler form must lift to integral cohomology. Such manifolds are called Hodge manifolds. The first example appeared in the 1979 article Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant and the general statement appeared 3 years later in Quantization of Newton's Constant in Certain Supergravity Theories.