Weak gravity versus scale separation

We give evidence that fully supersymmetric Anti-de Sitter vacua of extended supergravity with a residual gauge group containing an abelian factor cannot be scale separated as a consequence of the weak gravity conjecture. We prove this for N=2 and N=8 supergravity and we explain how our argument applies also to vacua with partially broken, but extended residual supersymmetry. We finally discuss possible loopholes and especially how certain N=1 models can evade our reasoning. Our results suggest that N=0,1 supersymmetry at the lagrangian level might be the most promising chances to obtain a truly four-dimensional effective description of quantum gravity.Comment: 23 pages, 9 tables; v2: references added, minor modifications, published on JHE