Metastable supersymmetry breaking in extended supergravity

TL;DR

This work extends the $s$Goldstino stability framework from minimal to extended supergravity by analyzing metastability of non-supersymmetric critical points in $\mathcal{N}=4$ gauged supergravity. It develops a covariant origin-based formulation using the embedding tensor and $F$-tensors to derive scalar masses and the sGoldstino mass, and shows that gravity-sector SUSY breaking generically destabilizes the $SL(2)$ sector while matter-sector breaking entangles $SO(6,n)$ scalars with sectional curvatures, precluding a universal no-go but allowing potential metastable vacua under suitable gaugings. The results provide concrete mass bounds and highlight the distinct roles of the gravity and matter sectors, with explicit connections to known examples and a pathway to the ${\cal N}=8$ case. Overall, the paper advances understanding of metastability in extended supergravity and informs string-model-building and holographic applications by clarifying when non-supersymmetric AdS/Minkowski/De Sitter vacua can be perturbatively viable.

Abstract

We consider the stability of non-supersymmetric critical points of general N=4 supergravities. A powerful method to analyse this issue based on the sGoldstino direction has been developed for minimal supergravity. We adapt this to the present case, and address the conceptually new features arising for extended supersymmetry. As an application, we investigate the stability when supersymmetry breaking proceeds via either the gravity or the matter sector. Finally, we outline the N=8 case.