Metastable supergravity vacua with F and D supersymmetry breaking

TL;DR

This work derives general necessary conditions for metastable Minkowski vacua in 4D $\mathcal{N}=1$ supergravity with both chiral and vector multiplets, enforcing $V=0$ and $\nabla_i V=0$ at the vacuum and analyzing a positive-definite Hessian. It shows that vector multiplets alleviate the flatness and stability constraints by adding positive $D$-term energy and effectively reducing the curvature felt by chiral multiplets; the strongest effect occurs when vector masses are comparable to the gravitino mass, with deviations translating into curvature corrections. The authors develop three analytic strategies (dynamical, kinematical, and bound-based) to extract actionable constraints, and apply them to heavy/light vector limits, simple scalar geometries, and string-inspired setups. The results provide concrete necessary conditions that can be used to screen string-inspired models for viable metastable vacua and offer guidance on how gauged isometries and vector multiplets shape SUSY breaking in supergravity.

Abstract

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum the scalar potential and all its first derivatives vanish, and derive a necessary condition for the matrix of its second derivatives to be positive definite. We study then the constraints set by the combination of the flatness condition needed for the tuning of the cosmological constant and the stability condition that is necessary to avoid unstable modes. We find that the existence of such a viable vacuum implies a condition involving the curvature tensor for the scalar geometry and the charge and mass matrices for the vector fields. Moreover, for given curvature, charges and masses satisfying this constraint, the vector of F and D auxiliary fields defining the Goldstino direction is constrained to lie within a certain domain. The effect of vector multiplets relative to chiral multiplets is maximal when the masses of the vector fields are comparable to the gravitino mass. When the masses are instead much larger or much smaller than the gravitino mass, the effect becomes small and translates into a correction to the effective curvature. We finally apply our results to some simple classes of examples, to illustrate their relevance.