Abstract
We study the structure of the supersymmetric moduli spaces of \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 2 supergravity theories in AdS4 backgrounds. In the \( \mathcal{N} \) = 1 case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In \( \mathcal{N} \) = 2 supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.