Weak gravity versus scale separation

TL;DR

This paper provides evidence that certain supersymmetric Anti-de Sitter vacua cannot achieve scale separation due to the weak gravity conjecture, implying limitations on constructing realistic four-dimensional quantum gravity models.

Contribution

The authors prove that fully supersymmetric AdS vacua with residual gauge groups containing an abelian factor cannot be scale separated, extending the argument to partially broken supersymmetry.

Findings

Scale separation is incompatible with fully supersymmetric AdS vacua with abelian factors.

The proof applies to N=2 and N=8 supergravity models.

Certain N=1 models may evade the no-scale separation result.

Abstract

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.