Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

TL;DR

The paper develops and sharpens the conditions for the existence of locally stable non-supersymmetric Minkowski vacua in four-dimensional supergravity with only chiral multiplets. Building on two necessary flatness and stability constraints, it shows that for factorizable and symmetric (coset) Kahler manifolds these conditions impose strong restrictions on Kahler geometry and constrain the Goldstino direction to lie in a cone, with explicit solvability in several symmetric coset cases. By applying the results to string-theory moduli spaces and the Randall–Sundrum radion, it demonstrates how curvature bounds translate into concrete criteria for vacuum existence and how various geometric enhancements affect (or do not affect) these criteria. The work also derives weaker, general necessary conditions for completely arbitrary manifolds, providing a framework to assess viability of Minkowski vacua across a broad class of supergravity models and pointing to the potential importance of vector multiplets and quantum corrections in relaxing the curvature constraints.

Abstract

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary conditions for flatness and stability derived in a previous paper (which involve the Kahler metric and its Riemann tensor contracted with the supersymmetry breaking auxiliary fields) we show that the implications of these constraints can be worked out exactly not only for factorizable scalar manifolds, but also for symmetric coset manifolds. In both cases, the conditions imply a strong restriction on the Kahler geometry and constrain the vector of auxiliary fields defining the Goldstino direction to lie in a certain cone. We then apply these results to the various homogeneous coset manifolds spanned by the moduli and untwisted matter fields arising in string compactifications, and discuss their implications. Finally, we also discuss what can be said for completely arbitrary scalar manifolds, and derive in this more general case some explicit but weaker restrictions on the Kahler geometry.