Metastable supergravity vacua with F and D supersymmetry breaking

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.

40 pages; v2 some clarifications added in the introduction; v3 some typos corrected

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• Globally and locally supersymmetric effective theories for light fields
• Supersymmetry and R-symmetry breaking in models with non-canonical Kahler potential
• Metastable supersymmetry breaking in extended supergravity
• Building a Nest at Tree Level: Classical Metastability and Non-Trivial Vacuum Structure in Supersymmetric Field Theories
• Perturbative Stability along the Supersymmetric Directions of the Landscape
• Simple metastable de Sitter vacua in N=2 gauged supergravity
• On the Effective Description of Large Volume Compactifications
• Soft masses in superstring models with anomalous U(1) symmetries
• Moduli stabilization with F-term uplifting in heterotic string theory
• Constraints from F and D supersymmetry breaking in general supergravity theories
• F-term SUSY Breaking and Moduli
• Mildly sequestered supergravity models and their realization in string theory
• Effects of heavy modes on vacuum stability in supersymmetric theories