Abstract
Abstract We study the possibility of achieving metastable de Sitter vacua in general N=2toN=1truncatedsupergravitieswithoutvectormultiplets,andcomparewiththe situations arising in N = 2 theories with only hypermultiplets and N = 1 theories with only chiral multiplets. In N = 2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N = 1 theories based on a Kähler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and the superpotential can be freely adjusted. In N = 2 to N = 1 truncations, the crucial requirement is then that the tachyon of the mother theory be projected out from the daughter theory, so that the original unstable vacuum is projected to a metastable vacuum. We study the circumstances under which this may happen and derive general constraints for metastability on the geometry and the gauging. We then study in full detail the simplest case of quaternionic manifolds of dimension four with at least one isometry, for which there exists a general parametrization, and study two types of truncations defining Kähler submanifolds of dimension two. As an application, we finally discuss the case of the universal hypermultiplet of N = 2 superstrings and its truncations to the dilaton chiral multiplet of N = 1 superstrings. We argue that de Sitter vacua in such theories are necessarily unstable in weakly coupled situations, while they can in principle be metastable in strongly coupled regimes.
Highlights
Which is directly interesting for model building, and the various cases of extended supersymmetry, which partly reflect some of the additional special features displayed by models with a higher-dimensional origin
We study the possibility of achieving metastable de Sitter vacua in general N = 2 to N = 1 truncated supergravities without vector multiplets, and compare with the situations arising in N = 2 theories with only hypermultiplets and N = 1 theories with only chiral multiplets
In N = 2 theories with hypermultiplets based on a quaternionic manifold with a triholomorphic isometry gauged by the graviphoton, metastable de Sitter vacua are excluded due to a sum rule satisfied by the triholomorphic sectional curvatures, independently of the gauged isometry [9]
Summary
As in the case of general N = 1 theories, the quantity m2avr defines by construction an upper bound to the square mass of the lightest scalar, and in order to have a metastable supersymmetry breaking vacuum with V > 0, one needs the sectional curvature R to satisfy the bound (4.29). In order for this to be smaller that the average mass, so that none of the two sGoldstini is tachyonic, the quantity e2iδZ should satisfy the following bound: e2iδ Z This represents another necessary condition for the existence of metastable de Sitter vacua, this time on the geometry of the space complementary to the Kahler submanifold. Some crucial restriction on the ability of tuning the superpotential to make the sGoldstino mass splitting sufficiently small already descends from the form of the geometry of the original quaternionic manifold, independently of the knowledge of which isometries this may admit
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